{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. 什么是ARIMA模型？\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 目录\n",
    "1. 什么是AR模型？\n",
    "2. 什么是MA模型？\n",
    "3. 什么是ARIMA模型？\n",
    "4. 如何用ARIMA建模？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 什么是AR模型？\n",
    "AR模型，也就是自回归。\n",
    "自回归很容易理解，也就是自己对自己以前的值做回归。最简单的AR(1),也就是自己对自己上一个时间点的值做回归。$\\epsilon_t$为误差项。\n",
    "\n",
    "AR(1): \n",
    "\n",
    "$X_t=\\beta_1 X_{t-1}+\\epsilon_t$\n",
    "\n",
    "\n",
    "AR(2): \n",
    "\n",
    "$X_t=\\beta_1 X_{t-1}+\\beta_2 X_{t-2}+\\epsilon_t$\n",
    "\n",
    "\n",
    "AR(p): \n",
    "\n",
    "$X_t=\\beta_1 X_{t-1}+\\beta_2 X_{t-2}+...\\beta_p X_{t-p}+\\epsilon_t$\n",
    "\n",
    "\n",
    "下面我们模拟一段AR(1)的序列,我们设定$\\beta$为-0.5、0.1、0.4、0.9。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD9CAYAAAC1DKAUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6c759e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "e=np.random.normal(0, 1, 100)\n",
    "beta=[-0.9, -0.4, 0.4, 0.9]\n",
    "for n, j in enumerate(beta):\n",
    "    ar1=np.zeros(101)\n",
    "    ax=plt.subplot(2, 2, n+1)\n",
    "    for i in np.arange(100):\n",
    "        ar1[i+1]=j*ar1[i]+e[i]\n",
    "    ax.plot(ar1, label=j)\n",
    "    plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "简单地看一下AR(1)的一些数学计算。\n",
    "自协方差与自相关系数：\n",
    "$$cov(Y_t, Y_t)= \\gamma_0= \\sigma^2  $$\n",
    "\n",
    "$$cov(Y_t, Y_{t−1})  = \\gamma_1= \\sigma^2\\beta_1$$\n",
    "\n",
    "$$corr(Y_t, Y_{t−1}) = \\rho_1 = \\frac{\\gamma_1}{\\sigma^2} = \\beta_1$$\n",
    "\n",
    "$$cov(Y_t, Y_{t−j}) = \\gamma_j = \\sigma^2\\beta_1^j$$\n",
    "\n",
    "$$corr(Y_t, Y_{t−j}) = \\rho_j = \\frac {\\gamma_j}{\\sigma^2} = \\beta_1^j$$\n",
    "\n",
    "$$\\text{Since }|\\beta_1| < 1$$\n",
    "\n",
    "$$\\lim_{j→∞}\\rho_j = \\beta_1^j = 0$$\n",
    "\n",
    "如果$\\beta$在-1和1之间，那么这个序列就是平稳的，因为相关性会递减。我们熟悉的随机漫步就是一个AR(1)模型，但是是不平稳的，因为$\\beta$等于1，也就是意味着$t_1$时刻的影响永远不会消失。如果$\\beta$的绝对值大于1，那么$t_1$时刻的影响不仅不会消失还会爆炸，来看一个例子。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAEDCAYAAAAVyO4LAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x83af1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e=np.random.normal(0,1,100)\n",
    "beta=2\n",
    "ar1=np.zeros(101)\n",
    "for i in np.arange(100):\n",
    "    ar1[i+1]=beta*ar1[i]+e[i]\n",
    "plt.plot(ar1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 什么是MA模型？\n",
    "MA(1)\n",
    "$$X_t=\\epsilon_t+\\theta_1\\epsilon_{t-1}$$\n",
    "\n",
    "MA(p)\n",
    "$$X_t=\\epsilon_t+\\theta_1\\epsilon_{t-1}+...+\\theta_p\\epsilon_{t-p}$$\n",
    "\n",
    "MA(1)方差：\n",
    "\n",
    "$$var(Y_t) = \\sigma^2 = E[(Y_t − μ)^2]$$\n",
    "\n",
    "$$= E[(\\epsilon_t + \\theta\\epsilon_{t−1})^2]$$\n",
    "\n",
    "$$= E[\\epsilon^2_t] + 2\\theta E[\\epsilon_t\\epsilon_{t−1}] + \\theta^2E[\\epsilon^2_{t−1}]$$\n",
    "\n",
    "$$= \\sigma^2_\\epsilon +0+\\theta^2\\sigma^2_\\epsilon = \\sigma^2_\\epsilon(1+\\theta^2)$$\n",
    "\n",
    "协方差：\n",
    "$$cov(Y_t, Y_{t−1}) = \\gamma_1 = E[(\\epsilon_t + \\theta\\epsilon_{t−1})(\\epsilon_{t−1} + \\theta\\epsilon_{t−2})]$$\n",
    "\n",
    "$$= E[\\epsilon_t\\epsilon_{t−1}] + \\theta E[\\epsilon_t\\epsilon_{t−2}]+ θE[\\epsilon^2_{t−1}] + \\theta^2 E[\\epsilon_{t−1}\\epsilon_{t−2}]$$\n",
    "\n",
    "$$= 0+0+\\theta \\sigma^2_\\epsilon + 0 = \\theta \\sigma^2_\\epsilon$$\n",
    "\n",
    "自相关系数：\n",
    "\n",
    "$$\\rho_1 =\\frac{\\gamma_1}{\\sigma^2} =\\frac {\\theta\\sigma^2_\\epsilon}{\\sigma^2_\\epsilon(1 + \\theta^2)}=\\theta(1 + \\theta^2)$$\n",
    "\n",
    "$$\\rho_j =\\gamma_j\\sigma^2 = 0 \\text{ for } j > 1$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 重点：\n",
    "$$ρ_1 = 0 \\text{ if } θ = 0$$\n",
    "\n",
    "$$ρ_1 > 0 \\text{ if } θ > 0$$\n",
    "\n",
    "$$ρ_1 < 0 \\text{ if } θ < 0$$\n",
    "\n",
    "我们模拟一段MA(1)的数据。令$\\theta$为-0.5、0.1、0.4、0.9。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlxj+L59MneEWmLZWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7e5a4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "e = np.random.normal(0,1,100)\n",
    "theta = [-0.9, -0.4, 0.4, 5]\n",
    "for n, j in enumerate(theta):\n",
    "    ma1=np.zeros(101)\n",
    "    ax=plt.subplot(2, 2, n+1)\n",
    "    for i in np.arange(100):\n",
    "        ma1[i+1] = j*e[i-1]+e[i]\n",
    "    ax.plot(ma1, label=j)\n",
    "    plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 什么是ARIMA模型？\n",
    "ARMA模型其实就是将AR和MA模型结合起来。看一个ARMA(1,1)模型好了。\n",
    "$$X_t=\\beta_1 X_{t-1}+\\epsilon_t+\\theta_1\\epsilon_{t-1}$$\n",
    "所以其实AR和MA都只是特殊情况的ARMA。那么ARIMA又是什么？比如ARIMA(1,1,1)模型，I的阶数是1，代表这个序列是**I(1)**,需要差分一次。当然你也可以先把序列处理成平稳的，然后直接用ARMA。\n",
    "那么为了确定模型的阶数，我们引入ACF和PACF函数。\n",
    "ACF就是autocorrelation function。什么意思呢？举个例子，$X_t$和$X_{t-1}$的correlation的值就是一阶ACF的值，$X_t$和$X_{t-p}$的相关系数的值就是p阶ACF的值。\n",
    "PACF就是partial autocorrelation function。以上面AR(p)为例子,一阶PACF的值就是$\\beta_1$,p阶PACF的值就是$\\beta_p$。 \n",
    "略过中间的推导，我们直接给出结论。AR(p)模型的PACF是p阶截尾的，MA(p)模型的ACF是p阶截尾的。  ARMA模型则ACF和PACF都是拖尾的。继续拿股票数据做一个例子。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3wAAAE/CAYAAAAdR8HJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nklRS/z/aCaIp+3I0VAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x563a8080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import tushare as ts\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "data=ts.get_k_data('000001', start='2016-01-01', end='2016-12-31', ktype='D',autype='qfq')\n",
    "data.index = pd.to_datetime(data['date'],format='%Y-%m-%d')\n",
    "\n",
    "data=data['close'].diff()[1:]\n",
    "fig = plt.figure(figsize=(15,5))\n",
    "ax1=fig.add_subplot(211)\n",
    "ax2=fig.add_subplot(212)\n",
    "fig = sm.graphics.tsa.plot_pacf(data,lags=20,ax=ax1)\n",
    "fig = sm.graphics.tsa.plot_acf(data,lags=20,ax=ax2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|模型|ACF|PACF|\n",
    "|:---:|:---:|:---:|\n",
    "|AR(p)|拖尾|p阶截尾|\n",
    "|MA(q)|q阶截尾|拖尾|\n",
    "|ARMA(p,q)|拖尾|拖尾|\n",
    "\n",
    "\n",
    "因为序列不平稳所以ACF没有衰减的趋势，可以很明显看到PACF是一阶截尾的。但是如果你用AR(1)建模会出现问题，因为序列不平稳。所以应该对差分后序列或者是收益率建模。但是发现差分后从图中依然不好确定阶数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里我们就会用信息准则法定阶，而个人更加推荐这种方法。\n",
    "常用的有AIC/BIC/，当然还有很多别的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda2\\lib\\site-packages\\statsmodels\\base\\model.py:473: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  'available', HessianInversionWarning)\n",
      "D:\\ProgramData\\Anaconda2\\lib\\site-packages\\statsmodels\\base\\model.py:496: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  \"Check mle_retvals\", ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>ARMA Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>close</td>      <th>  No. Observations:  </th>    <td>232</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARMA(2, 3)</td>    <th>  Log Likelihood     </th>  <td>206.512</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>0.098</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Thu, 18 May 2017</td> <th>  AIC                </th> <td>-401.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>16:21:51</td>     <th>  BIC                </th> <td>-380.344</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>           <td>01-06-2016</td>    <th>  HQIC               </th> <td>-392.685</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                 <td>- 12-16-2016</td>   <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1.close</th> <td>   -1.9161</td> <td>    0.035</td> <td>  -55.219</td> <td> 0.000</td> <td>   -1.984</td> <td>   -1.848</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2.close</th> <td>   -0.9701</td> <td>    0.032</td> <td>  -30.224</td> <td> 0.000</td> <td>   -1.033</td> <td>   -0.907</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1.close</th> <td>    0.8393</td> <td>    0.074</td> <td>   11.271</td> <td> 0.000</td> <td>    0.693</td> <td>    0.985</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2.close</th> <td>   -0.9613</td> <td>    0.066</td> <td>  -14.500</td> <td> 0.000</td> <td>   -1.091</td> <td>   -0.831</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L3.close</th> <td>   -0.8778</td> <td>    0.069</td> <td>  -12.737</td> <td> 0.000</td> <td>   -1.013</td> <td>   -0.743</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Roots</caption>\n",
       "<tr>\n",
       "    <td></td>   <th>           Real</th> <th>         Imaginary</th> <th>         Modulus</th> <th>        Frequency</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.1</th>              -0.9876                    -0.2357j                    1.0153                   -0.4627     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AR.2</th>              -0.9876                    +0.2357j                    1.0153                    0.4627     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.1</th>               1.0001                    -0.0000j                    1.0001                   -0.0000     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.2</th>              -1.0476                    -0.2041j                    1.0673                   -0.4694     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MA.3</th>              -1.0476                    +0.2041j                    1.0673                    0.4694     \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                              ARMA Model Results                              \n",
       "==============================================================================\n",
       "Dep. Variable:                  close   No. Observations:                  232\n",
       "Model:                     ARMA(2, 3)   Log Likelihood                 206.512\n",
       "Method:                       css-mle   S.D. of innovations              0.098\n",
       "Date:                Thu, 18 May 2017   AIC                           -401.025\n",
       "Time:                        16:21:51   BIC                           -380.344\n",
       "Sample:                    01-06-2016   HQIC                          -392.685\n",
       "                         - 12-16-2016                                         \n",
       "===============================================================================\n",
       "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "ar.L1.close    -1.9161      0.035    -55.219      0.000      -1.984      -1.848\n",
       "ar.L2.close    -0.9701      0.032    -30.224      0.000      -1.033      -0.907\n",
       "ma.L1.close     0.8393      0.074     11.271      0.000       0.693       0.985\n",
       "ma.L2.close    -0.9613      0.066    -14.500      0.000      -1.091      -0.831\n",
       "ma.L3.close    -0.8778      0.069    -12.737      0.000      -1.013      -0.743\n",
       "                                    Roots                                    \n",
       "=============================================================================\n",
       "                 Real           Imaginary           Modulus         Frequency\n",
       "-----------------------------------------------------------------------------\n",
       "AR.1           -0.9876           -0.2357j            1.0153           -0.4627\n",
       "AR.2           -0.9876           +0.2357j            1.0153            0.4627\n",
       "MA.1            1.0001           -0.0000j            1.0001           -0.0000\n",
       "MA.2           -1.0476           -0.2041j            1.0673           -0.4694\n",
       "MA.3           -1.0476           +0.2041j            1.0673            0.4694\n",
       "-----------------------------------------------------------------------------\n",
       "\"\"\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# order=sm.tsa.arma_order_select_ic(data.diff()[1:],max_ar=5,max_ma=5, ic='bic')['bic_min_order']\n",
    "# order=sm.tsa.arma_order_select_ic(data.diff()[1:],max_ar=5,max_ma=4,ic='aic')['aic_min_order']\n",
    "# order = sm.tsa.arma_order_select_ic(data,max_ar=5,max_ma=4,ic='hqic')['hqic_min_order'] # HQIC\n",
    "train=data.diff()[1:-10]\n",
    "# print train\n",
    "\n",
    "Model = sm.tsa.ARMA(train, order=(2,3))\n",
    "arma = Model.fit(trend='nc', disp=-1)\n",
    "arma.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 计算模型得分\n",
    "模型得分越接近1越好，以下结果为0.58。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.58016828658\n"
     ]
    }
   ],
   "source": [
    "delta = arma.fittedvalues - train\n",
    "score = 1 - delta.var()/train.var()\n",
    "print score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             predict  actual\n",
      "date                        \n",
      "2016-12-19  0.047925   -0.05\n",
      "2016-12-20 -0.042729   -0.04\n",
      "2016-12-21  0.035379    0.14\n",
      "2016-12-22 -0.026338   -0.07\n",
      "2016-12-23  0.016144   -0.04\n",
      "2016-12-26 -0.005383    0.10\n",
      "2016-12-27 -0.005347   -0.08\n",
      "2016-12-28  0.015467    0.02\n",
      "2016-12-29 -0.024449    0.04\n",
      "2016-12-30  0.031841    0.00\n"
     ]
    }
   ],
   "source": [
    "Y = data.diff()[-10:]\n",
    "predict = arma.predict(start=(len(data.diff()[1:])-11),end=len(data.diff()[1:]),dynamic=True)[-10:]\n",
    "\n",
    "predict.index = Y.index\n",
    "chart = pd.concat([predict,Y], axis=1, keys=['predict', 'actual'])\n",
    "print chart"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmUAAAHVCAYAAACwrYzPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlAkhhBBCmIAkZUIIIYQQJvD/AampPqZohjmYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5fed31d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,8))\n",
    "ax.plot(chart.predict, label='predict')\n",
    "ax.plot(chart.actual, label='actual')\n",
    "ax.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD8CAYAAAB+UHOxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvXeYJUd97/2p7j5pzuSd2byrVc6IIAQmGplgMFjc9xqD\nsMHYFzC24fo1Ntf4NTZc2/gaYxuwSQZMfE2QLMACRDBJCAWkVUTSrqRN2jS7k8OJner+UdXd1eec\nmZ3ZmVlpR/19nnlm5pwO1aHqW99fKiGlJEOGDBkyPPFgPdYNyJAhQ4YMjw0yAsiQIUOGJygyAsiQ\nIUOGJygyAsiQIUOGJygyAsiQIUOGJygyAsiQIUOGJygyAsiQIUOGJygyAsiQIUOGJygyAsiQIUOG\nJyicx7oBC2FoaEju2LHjsW5GhgwZMpw2uPPOO8ellMOL2fZxTQA7duxg586dj3UzMmTIkOG0gRDi\n0cVum5mAMmTIkOEJiowAMmTIkOEJiowAMmTIkOEJiowAMmTIkOEJiowAMmTIkOEJiowAMmTIkOEJ\niowAMmTIkOEJirVLAFLC3f8/+M3HuiUZMmTI8LjE2iWA4w/Af/4B7P3hY92SDBkyZHhcYu0SQOip\n35kCyJAhQ4aOWBECEEL8shDiISHEHiHEO+fZ5heFEPcIIR4QQty4EuddEDLUv4NVP1WGDBkynI5Y\ndi0gIYQNfAR4EXAYuEMIcb2U8kFjm37go8AvSykPCiHWL/e8J4TUv8OMADJkyJChE1ZCAVwB7JFS\n7pNSusCXgatatnkt8FUp5UEAKeXoCpz3BNAMEPqrf6oMGTJkOA2xEgSwBThk/H9Yf2biPGBACPFj\nIcSdQojXz3cwIcSbhRA7hRA7x8bGTr5VMiOADBkyZFgIp8oJ7ABPA34FeAnwF0KI8zptKKX8hJTy\ncinl5cPDiyppPQ8yAsiQIUOGhbAS6wEcAbYZ/2/Vn5k4DExIKatAVQjxE+Ay4OEVOH9nxAog8wFk\nyJAhQyeshAK4AzhXCHGmECIPvAa4vmWb/wSeI4RwhBBdwDOAXStw7gWQKYAMGTJkWAjLVgBSSl8I\n8Vbgu4ANfFpK+YAQ4i36+49LKXcJIb4D3AeEwKeklPcv99wLN0yHgWYEkCFDhgwdsSJLQkopbwBu\naPns4y3/vx94/0qcb5GNUr8zAsiQIUOGjli7mcBkPoAMGTJkWAhrlwAyJ3CGDBkyLIi1SwCZEzhD\nhgwZFsTaJYDMB5AhQ4YMC2LtEkCmADJkyJBhQaxdAojDQDMfQIYMGTJ0whomgEwBZMiQIcNCWLsE\nkJmAMmTIkGFBrF0CiNcDyAggQ4YMGTph7RJAlgiWIUOGDAti7RJA5AM4XZaEbMxCkKmVDBkynDqs\nWQIIQxUFFPjeY9ySReJjz4affeyxbkWGDBmeQFizBHBoqgLA2Gz1MW7JIlE5BrMjj3UrMmTI8ATC\nmiWAMFAmIHm6mFVkCOFpolYyZMiwJrB2CeB0Ww9ASgjcx7oVGTJkeAJhzRKADLUCOE0IQMqQidPF\nXJUhQ4Y1gTVLAJECEMsIA214AfcfmVmpJi0IgeTo5NwpOVeGDBkywJomgOVnAn/97iO88iM3U2mu\nsorQbRVB5gPIkCHDqcOaJYCVqAVUafr4ocT1wxVq1DyICEBmBJAhQ4ZThzVLAKE2/SzHBBSpiFhN\nrBYic9XpErGUIUOGNYG1SwArkAkcRiJilQkgSlqzMgWQIUOGU4g1SwAyXP56AEEUSbTKAiBRK5kC\nyJAhw6nD2iWA2K5+8oOq7dd5stgTE8FqIVYAWSJYhgwZTiFWhACEEL8shHhICLFHCPHOBbZ7uhDC\nF0L82kqcdyFEeQBiGSagc45/m//IvwfZXN3wzChk1VoGWWXIkCHDUrFsAhBC2MBHgJcCFwFXCyEu\nmme79wHfW+45FwMZDarLMKs4fg1HhJQe+hrc9vGValobIhNQRgAZMmQ4lVgJBXAFsEdKuU9K6QJf\nBq7qsN3bgOuA0RU45wkRyuUrAFAk0rXrP+COT61Aq+Y5i1YrduYEzpAhwynEShDAFuCQ8f9h/VkM\nIcQW4L8Bp6zeceQEXhYBmPWEVtE+H/kA7EwBZMiQ4RTiVDmBPwj8qYzsMgtACPFmIcROIcTOsbGx\nkz5hbAJaBgHI0EgmW8UYfRkrgIwAMmTIcOrgrMAxjgDbjP+36s9MXA58WQgBMAS8TAjhSym/3now\nKeUngE8AXH755ScdfhNFAS3Lrh7XE/JWWQEoksoIIEOGDKcSK0EAdwDnCiHORA38rwFea24gpTwz\n+lsI8Vngm50G/5VENKtelgIwTUCrWKcnigKyyQggQ4YMpw7LJgAppS+EeCvwXcAGPi2lfEAI8Rb9\n/eqFzyzYLj17Zxl1fMx6QquYpBUpAOd0Wb84Q4YMawIroQCQUt4A3NDyWceBX0r5hpU454kQyuUr\ngMQEtLoKIDJXOZkCyJAhwynEms0EjgZve0UIYJV9AIE6T0YAGTJkOJVYswQQl1dgBcJAA20CWqWi\nQJEPIM/qnSNDhgwZWrFmCYDYrBKc9KAa1xOKZv+r5QcIDT/FMorXZciQIcNSsGYJQJqD/onTDzpC\nmD4AWDU/QGi0T2YLw2fIkOEUYc0SQKqGf+jDfdfAT96/pGO0K4DVIYAgSAjA95qrco4MGTJkaMWK\nRAE9HpFKOg59+Oqb1N/Pe8cSDhKVk4gUwOqYgKRhAvI8l9yqnCVDhgwZ0lizCkC2KoCTQkQAUULY\n6igAk6x8NzMBZciQ4dRgzRJAyvF7so7VVt/BKtnn0wogMwFlyJDh1GDNEoBcicia1uihVXICB6Hp\nA8gUQIYMGU4N1i4BsAImoFYFsEphoLKVAGaOwG2nrHJ2hgwZnqBYu07gsMUJfHIHSf+/SgrA9FcE\nXhOufQMcvh3OewkMnrUq58yQIUOGtasAVsIJ3GoCWjUncGKi8j0X/Lr6pzG7KufLkCFDBljLBMAi\nncC7b4DPXzVPtnCrAvChWYGPPguO3rP4xtx3Dez65rxfR0tCglYAhV71zyovRp8hQ4YnNtYuAZiD\n6kKmmy9fDft+3FEliE4K4NBtMPoAfP89i2/MbR+Fnf82f1sNBRD4LuS71T9udfHnyJAhQ4YlYu0S\ngBlb7y3CdNNJAXT0AYilNyb0F1QhKR+A70EhIoDK0s+VIUOGDIvEmiUAYQzeCyqACB3qBckFfQBL\nKDAXBgsTgFEKIvQMBdDMfAAZMmRYPaxZAjBrAS1OAbQTQNtqYoEPQiuApVQYPcGKYoFJVr4LhR71\nz2qbgL72FrjlX1b3HBkyZHjcYu2GgZoE4J8cAXSOAipEXy6+MSdaUtIIWQ19Fwol9c9qO4EP3Ax+\nlnmcIcMTFWtWAZiDd7iYIm6dFEAnH8BJKYCgnQB8Fyqj+lBGW30jE7gxs/hznAyC5kmXys6QIYVH\n/guue+Nj3YoMS8SaJYB5FYCZINa6ZsAXXw3f/9/mUdIHDX1OzgncwQew89/gw0+HMEw5rEPfS7Zd\n7TwAvwnZQvSnN+aOgVt7rFsBB34K91/3WLciwxKxhgnAtKsbs29zwDNNLDKEsYdgdFf6MxOmAlgK\nOpmApg5AYxpkiDTIQQZect7VdgIHXpoQM5x++PRL4KZ/eKxbQRj66r3NljQ9rbBmCYDW0MoI5ky8\nPpnePvRToZdtJqDQCANdrhO4Pq2PE6YSwaTvJiTVmFEJZHt/uPhzLQWZCej0R3UCph59rFvBg0f0\n+5wtaXpa4QnhBA4NApChnxhxaiYBBGpGbKgC0WoCCk42DLQTAUwB8M//tYuH79vH0+NmeAm5NGbU\n7K40AGdfufjzLapNoV7oPuuwpzVkkJ7IPEaoNZTvSoY+wl6zw8qaw4ooACHELwshHhJC7BFCvLPD\n978hhLhPCPFzIcQtQojLVuK8C2KePIDAdAinFECoZvhG6GVbHsDJOoFl2D4z0gTwsRv3MDJdTzYN\nXBqubm9zVu23GpE6QTNpW4bTF6Gfnsg8RpB6grOoiLsMjxssmwCEEDbwEeClwEXA1UKIi1o22w88\nX0p5KfDXwCeWe94Tw1QAyaAfBMlAvP/QYWPzUMX5L9YEtFwF0FCS2UJimccKPPaPKdt/WJ9R7fIb\niz/XYhGRygpJ9prrc9fBqRU51rIxfQje07dg/aU1g9B/XCiAqPqu769OyfQMq4OVUABXAHuklPuk\nlC7wZeAqcwMp5S1Symh0uA3YugLnXRBmLaDQUADSUADHxifMHdoUQHsimJfefrFYwARkE6ZMTTLw\nCDVJichGvxIKwGvATf+owk8huZYVMgFdd9cRXvXxW6k2HwcDwNG71e97v/TYtmO1EYbq/ag9DohX\nv9/eKq2bnWF1sBIEsAU4ZPx/WH82H/4H8O0VOO+CMKuBmmYfMycgcI2ZtQwTJ3Bk3mlLBPNZ0szf\n3M8kACljJ7BAYglTAbiJ6UlKbQJaAQVw8Fb4wV+pYnZgmIBWJmqjWqtyhjxC3Xsc+BQiUhNLeL1n\nR5RD9XRCdJ3uXELsEXZ+Wv2cqqZoJRksJus+w+MGpzQKSAjxAhQB/OkC27xZCLFTCLFzbGzspM9l\nhoGas/7AMHmErQQQhWB6yibf0QkcHXexA6eU7T4AtxrXFbJaFAChj4g6tgzUz0oogIiAIoWzwiag\n5+3+W35Y+BO8ufEVOd6yED2jpRDAP10A7z/NFt8xJxX1FhVw97/DPV9M/pdydRMLIwJoNQGtdjJj\nhmVhJQjgCLDN+H+r/iwFIcSTgE8BV0kp551qSSk/IaW8XEp5+fDw8Mm3KrUcQPJSSsMHEHqJ8/WH\nDxxJdtJ+gE4+gLqrjlVzFyl1owHW7Kza/g9gI1sIwEvIS4YpQloWWgkgWuB+hZzAm2fuVIetPh7M\nEfqaLPuxbcdqI0UALX4At5LOc7n7C/B321Wuy2pAT1pSJqCxh+B9O2DkvtU5Z4ZlYyUI4A7gXCHE\nmUKIPPAa4HpzAyHEduCrwOuklA+vwDlPDDO71rDdp8jAMK2871vGSxo7glsVgM90Tc2c64smAD/9\nG1KzNdGiAERgZAJHGcQrqgD0tUXHXCEfQCBy6rd3cm297s7DvPFzO1ekLYkJaG0TgKls2yKBmi0E\n8Mj31G8z0XEl0ckENLFX9cO5Y6tzzgzLxrIJQErpA28FvgvsAq6RUj4ghHiLEOIterO/BNYBHxVC\n3COEWKGevlDDOpuAQmMgFl5CAHmMztSchwBCjzAu3bxIE9AJCKA1CkiEiZlJIFcuCigiwVYFsEIm\nIF+o2G/Pc0+wZWfcum+C7+86jhesgCKJrmmNK4A4XBjmUQDGehIRGa5W2K8m3VQUUE0L/VVaSnWt\n4qM/3sNvffr2U3KuFcnYkFLeANzQ8tnHjb/fCJzSSlFmDL8MO5uAZJDMVvMYL6keJDsWg4vt80sk\nABmofYRIsoBpjwJSBGDwcuCpDhQG8YDmBSGVhs9AOb+4NgCHJ+fYCoxPTTEEK24C8vWr5Lc6IxeJ\n6Zrab7zSZFNfaXmNWWsK4EOXwbP/EC7/ndTHtWaD+E7VzIg2qQggNN65yB+yWgQQ+wCMfhS1aTHr\ncWSIcWC8ysPHT81ysGu3FISBcD4FYMys88KYuUQ+gA4KIIp3Hpx5AD72nPQsq/PJ2/82FMDVzg95\ng/3dpE2mE1ifE0iZgb50+0Gu/McftyeqLYDZqvIjVGan08dbMROQIoCguQh/xVd/F279SOqjyaoi\ngOOzK2HuihTAGni9pVR1o775R21fNRoG2ZomIL+ZRKxFim+1CUAfN+ioALLQ0KWg6YcUnFPz7q6B\nHtIZ80UBhUbxM8tQAAVTAWjbabsC8OP9BRKO/xwqx0/QEHMw1+0wnMCvtG7mSjtZYF4pADMsVO9j\nkNXx2QZTNQ8vWDwBRB0zbLaagJYwIIzugps/lP7Mb8L33oUdquOFi3FY7/0BHL4j9dFUTd3/0dkV\nMHedTBTQ4xULDNi1hkGWpgnIXEhIv8syIsPVqtUTmYDCDn6JTAEsCQ0voJg7Nep1DfSQeSAlPuom\nylQUUPK3dQITUCcfgGydMZ/o5TY7RPS3oQAckT6eZaiM6JxASgFEA7+/hME7Kochm61O4CUQwP3X\nwX/9ZXoQGbkPbvkXtjQeUYc7EQFIqa6/xVQUK4C5FVAAMQGsARPQAgN2o5ncK2kqANcwH2gC2D+h\niPXYzOqsMmfpfhGuBQUwdxy+82fJ5OsUYPexWXa881vcdXCK50x9jT+t/9MpOe+aJQCJjM0Spg8g\nNHwA0awVWpzAcRhomgBk4EHYTgoLoiMBJArAIf2SWdJHYHT6iGAMBeD6aoDz/KUrANkWBrqEGWHU\nfpP0Wjp36J6AANyK2idI7r0fhMzUV1ABrCUn8AKDZ71p3MOK4QMwzZKaAEZm9f2dWYGQ4k5YwAcg\nTzcF8K23w20fVUr1FOHWvepeff3uI2xu7OEy795Tct41SwBChkgEvrRSncgkAzucTwFEPoD07DgM\nlqsA2n0AOWOwd8lhRXXV4306KQBNAEtQANFKY5Z3EnkA43vg48+FmSPpfc32aUjvBAN4dO3GMabr\nyTFGV8IHsJacwAsQdNNQAKGZxZwyAek1JbQ5LFwlE1A0aTGz7puzKpHz8MQqr2ux0uiUu7PK6O9S\nYdTTNQ8R+oTi1FRUXbMEoBykggA7ZfYp774WjtwFgCMNBWA6gZudncDS91I+BODEL0nYwQeQIoBk\nf1/ksKXXeVD2k5lbrACWEDIZOcJjAlhKJvDdn4dj98HYbr1PB1WjcUITUAcCmKomf285/gPYd+OJ\n27QQVlsB+E144GsrVkZjQSzwfjVcdd88aSPNTOAOJqDIIS5XiwD0O5tafrWuSKle7zApkBIe+Hp7\nCYtTibljnd81cZL+kl3fSJPvEtBd0ARQ9xChlxHAsiGlUgBYqVl7//2fg0++AC8IyUsPV6pBonMY\naLqDh4HbPiM7oQJY2AnsGArAEzksGbQ7nwH8JlJKdo3MxgO/vwQncJQM5wR6+cDFmoCkhPu/phtY\nT+8LjGubchhVST0ZAtAO4FLO5n+OvQc+/6sLH+NEOJlaQEvBg9fDtW+A8UdW5/gmFlB5TZ0HMEEv\nlukE7mACiu6FXKUV4KLItcDX9z7wKXi6qm2nPrLvR3Dtb8EP/3pV2rMo3P5J+NJr2j+3TiJiauYw\nfOU31cTgJBBo0/JMzVUKwMoIYFmQqPjnEKujM6fmBhTwaFAA5vEBtJiApO+mqowCJ+kDmIJ8D5A2\nAQUijy39eRRAg2/eN8JLP3QT37hvBFiEAmjOxevFRjOzXKAG6GpNz1RONIs9vBNmDuo2aNVgDN6T\nc/r4UsTtXBAdCCByAO9Y17XwvotF9LwXSwDzrRM9H6L74S4hVttrwGdfnlQqXSwWVADqeYzJPhx3\nJmm7Oz8BrJZZI1YAUX8wJjkdCSDyg00/hquZuRXwau0kezIhs9HMvzUj+0f/B+76fPL/yL3w5d9o\nmzhGfVkpgMwEtHxIVQ80EHbHl77m+hRxqaOSqTr7ANqdwG021JOKApqBrkGAVCVQ31ImINFpVu43\neWRUtSuaLZwwDPSLr4njxyMzWD5UBPDxH+iSACeSuQ981WhDpACSa44Sv6J7FWdXh6F60Q/8NH08\n3fG9ZkIUUzoJ7JLBFRqcokFo0QQwz5KhERqz6ifC7FH1eyk1mo7eDQdughvesfh9YEGF5jZVu8dl\nn4rCiQqvdQgDjfwhbe/v3LFlR7v4QYitJ0txFJCRmNaRAKxVzkxeDDpMaICTI4DoWK3F7+6/Dh76\nTvL/gZth9zehmi50GUX0zdQ9LOkhMwWwTBg+gE6duuYGFIRHXSoFUOjgA2ibDQZ+Kr9AfbYUE1Cg\nOltzhord176pyGPjd56F+g1yVnpB+gUVgFdXpZ+ro0ASiVEI1cCbi653gZf8Mz/di3vvdTCwIzkm\npK45qv1iayITWmHgVtSL/uit6YNqBTBTqcUfRQrgovIKZT8uMcs5FaUSdHBC/9029RMhJoAlRCx5\n+npzS8tyDhcYnF1ddmNc6ncpMgOZg37kBO404DYr8I/nE3zrj5fUprZ2BCGWJoDICexXjAGuUx+J\nHPSrZJJaFFaSAKJrbLY4vP1m+vjRJKpl8hBN5qZrHlYYIK3c4s+9DKxdAkAihUXIPAqgGVDooAD8\nXHc8g7I6KIC2l2KpJiA9Qzjml9s2DawcjvTn9QHYdpoA/FZzlImRezHXIYgGkiINCMPE5LXADPMn\n37+efP04XPrr+oR6wDNe6KBlCUDRuk3LgBo5Ky2Z7DdVdSnlbLZbK7Sy1RIXu2maNXVaB4MOqI4p\nE1ClshQTUEQAXWoR99s+tihzk2fe35bB0tVO4EnRrz6IFoZxK2A5SmW2+QCSe1Kra//Nvdcs/jo6\ntlEmCkCHWY+PjsTfdwwDjQnpMVw/IpiPACJyWoIyCuZRAH4j3V+iTPkWU6npz8sUwEpAhoAgEDZC\ntj/Iqut39AF4ud55fQC0JmnBiRVAayawto1O0dO+qZXHntcJ3CDXUtpgQQVwWNfbi9obROsPSPDr\nSebzAiagFwa30CAPF748aT+kSK+19o8V6Bc7ml21VDL1dLy6Y+RgTNZcBst51oVq1hjmuue/rsUg\neiaLnF3W6sZsbBEx64EOh52eXUKt+8jmnSspR+F33qkchydAqriaV0t9FxXeq+YG9Dk0gbpVyHdD\noTfJau/gBJ7T5UGcYHm5Ac0gSAhAvyNTYwYBLLRO8GplJi8G8ymAiJyWUoQxNgEtrAB2H1HveKWS\nLiFjJnXaBJApgGVC+wDmVwAeReFRl2kF4Ob6oFlBStlxQZi2MLoThoG2KAA9A54I2wkgtPM6MWwe\nBbAUE9CRiAB0ApjRjqBRMRRA52P4Qcjzrbu4MXwyQb43/aVZXrulc1vRyx51nvFH4IOXxjkE7pwa\npGyDlKeqLgPlHAO+Mlf5+fZ7syQsMcnNTKg6UentuUqF3mBKn6Zl4KyOw4eeDEfvad8xsonnupL7\nN75Abf6fvB/e00f+229PPmsjAHWcen5QnyMyAVWg0KN+4jBQ7QMwTEoR8bW950uE6xs+AH38uUlV\nIqUhc6l3L0as0h4HJqCWZ35wSt2X6dkTKLwb/15F/kDyzrUqgCBNAJU5dcxarQKf+1W49reBtD8v\nR6AU3CnA2iUAlA8gFJ19AFFscq1FATSdHnArhDLdMRoyhwg72OeXmgimZ4LHO5iAQksRwLwKwG4l\ngAU6bqQAokHQaEetMhMTXptPI9rGC+ilxtFwgGNzLR3YzOJtI4AWE9Cxn8P0QZjcpz7Wg5RtON2n\nah4DXXm6m6N63wXu6c5Pw57vz/+9uf8iBxezpMKJTEA/uev++O+2rOdDP4Op/Z0XXTGrdUbnMLab\na3iEpknv4M8AsI//PPnMTc8aXU0AbnFIfRApAK8G+XKKAKQO05WGYkspn1aM7lYlERYBL5CxDyAK\nNmjOjlGjQIWSeh7VcTiW3LuZijI/zdZPMvFv/01Jv54dObmFbuYxAe3TZTMmZk6QwPbwd5SD13cT\nEjF9AFKC36BSS+5zQ5vdvEYN9t8YB1mYkzkHH+xMASwPugxuKGw1cLeg2VAPIjIBRU7RRkwA6Tr9\nLrnOtYBO6ANoMQFpBXDUbQ95lHaeHPObgGxtAsrjsZ4p/OilOXS76mAR5o7DjFqmWYY+f/61nzM+\nm8wea5WZJPFtnllyww3I4dMkx4GplkExtcBO+vrt2ASkf0cdQncyoa/fMRWANgGVmuOpbU386KFR\nPvmTfXDTP6n47QizI+kwO0ieySLNC/UUASz8PHf+3CSAlqSf4w+o351MB9Hs3Ksn7dODVt0NuPQ9\n3+P/fNtYrKWiFlER5uy05XyRCUiWBlUehnkOp5gyAUVkaNrjG40FCOArvwE/eu/83xtIKQB9z8Pq\nBBWrTyVihh58+Onw8WfH+4xMqnal1NdiMf4IfO7lKsgAVC7BNa9f8mF8t92nBUkFMEcu8C5ICWMP\nq2c5/nBnBaA/G5lIPnMbqh/69bRS8FMEEGQEsFxInQgWCLtj9mNDz358qwhAUQ+IdbsHApfAa6YI\noImDCP0l+wAC00Zu+ACONNsJQCmAoJ1kALwGjlYAf5f7JLcX/wDfc9VC5p95qapdEiEy/5QGCIOA\nf//ZQXxjpaZ6dTbJQA5D1aFa7lHNDcjj4eGwb6pllraACSgurxFddzQA6X3sprp+hyC20U9WXQa6\n8uQbigCsDpE4X7vrCJ+8aR9efY7GhBE7/vNr4Pq3pdfE1R3vwPgcO975LSYqC88yG2ZVzdZzG8/v\n2EyD8aP74/+l2zLQH/t56vwpRArAbyT3TxNApamexZdvP5RsX1FqSATGOdy0CWhOr05XLHYxR3da\nAeS6tALQBBx2IoAFbNy1ibRqWQAmAUTHtxuTNPMDBNiIwG9bsGauqsisbQ3hxSAiOq0qqU+pHynh\nW38MD38vvf1916YnDRp7R6Jn0vK89L2yF1KDs0eTPJDj93cOA9UTgaiveUFIoCPH7Il0EqHVnOFD\nuQ+zkQk1CcwIYLlQJiCJ3TGu3mvqBCYnTQBVS9m7ZbOacgI3ySPM9XojnIAAXL+zD2AsaDcBKQXg\nIzo5L/0GllAE8EJLlbKwq8dg9zfUcc0ElMM7lQ1x81Nj048jkmM2KrOxCUj4dfjoM+GnH0idrt50\nsYXElQ57J1oGCqNjtBKAExNAtI9M7ZPzDIkcuHhByFzDZ6Arj11XBGCHbpupreYG1NyA0K0SThkD\nZUQwpvNNP5N9o+qz3ccWtuU23eR6ZOtg4CWz7uvvPcJG1H0OpUD6LTPoBRWAHmy8mkEAu0FKVf6X\nJs2oUGEYtMWJAykTUMML4nLQXcUC03SnFUCulDIBhboPiKAZh6/WFyIAt9pmcpp30yDEEhEBBMw1\nPLqDGWRpUBVk7KCSZ6uq/wUn4wSO2hU50b2aIkevBnd8SmUYHzNMZ199I9zwJ22HiZ613xKSGfmn\nRKeQ4AhRWRRQBBBt25yLCSTUE4S8UNd/dLpOQart8pNpk9Xw7P1cZd/CVwvvxskIYAUgJVIIpEgX\ng4vg6nAc5UBoAAAgAElEQVSswFZx2QX9kCqWikAJmxVMi7srlQJojSw5Ornw4OKZIYZhAPUpwlw3\nbqfF2Jw8ORF0Nsv4TUI9KM5IRR756tEk9dzsrEd2woaLlR1YdzDbyDhu1ufSmc+hr2ZIBpnVtXnA\nEw57xls6gtGhZUucujNfaF3ogdcgHzaYlN3xNlES2LqSQNQmCaRQvpeWZ1ZzfZpukwIeXWElGfAj\ns4i5/m2U82Cp+zXXWHiWaRZV81vXNDbMLl+7+yhP6q0S5ruZpSsdy+1WkxlpJ0dyTACGCagxDZVR\nGo06u4u/zf9Cm7KqY539F0Zbjk7X4zIi3aUCE2E5KQndSgBSIvR78KyJ6+ATz1fXbRKA+V4HHgQu\nbm1xRdzSJiCf/eNVBpjD6RkiwE5HGelnU6lFGeonQQCRMzwmgLoi6sgM6tXgS69Nm0U7IA78aKaf\nVxSivGBhw8jn0LtF+UviiYOMVVd0jZECODBRo6jP2TWdXhrdD9Vos1lMsklMZASwXIjYCezEtcpN\n+NoH4GoTUF4/9IpQg5NszsWOLYAmOSzZngjmugubF1Jr5IY+1Kfx8r1J7RwD0lb+CFt6qoppusFJ\nvRAUAfRMPaicYRgrfYUBHLkbtlwOloMMfV5m3cZmMYGnScerz8WEF6NyDB78z+R69eDQUy7zyFjL\nTDcwCSA90Of0DCcuNWHuo81fY1LHrQcuU1V1rA25KiA5Lob19abv62BtPy80l5Ke1ZVJI+Ibf0gt\nQq6PC5C3Jb1UyR+7i4XQMJ6h32rWMcwuu0ZmOa80S9i9WYXHmgpgdBetaicFQwGk3pmx3TSrasB4\no/Nt9Vm0yJDdsuSnEQV0ZLqOrWfd5VKBKdlDaKqMyAQUerqOlPHejj0EgU/TyMamaZguNNE8OjLa\nfh0d4BqZwDIMFAGIOUp96wmEw7qmEe6q1VFNB2G0TiAWg3hNC1MBmIvPP+8dKgHymtenCaZl8hb1\nAbfZWQHIEymA0iCsv1CZt8xtNQHM6TyRaLL16ESVolDvRvecfleFBVKmorMKwsfKCGCZ0E5gOU8e\ngKc7um8rAshpZp7Vg6tsVtqcwKK1VDOc0AmcipLRJqBmro+g063XHT4nvXgxm+RAzZgAZqXyH5y9\n/4sgAyZkDxOTuvOPP6xsk1svB8tGNOf4aP6feYa1m5qlrs1rVQARbv9Ecr26Uwz39XC81mr2MkxA\nLR04p01AXkunmq1WE/NXlLkauHEW8LBQnWbcHm47B8BVlWv4UO7DSRMiM1A0K77+D5PCXpqgSsLn\nlsLbuPKnV6cVQgtMldauANJmkD5vDHo3U5f5pOwFpE0OrSag+nRSG8er8+joTBx+zNhDNM175dXj\n6JuZ/Pr0caIBDjg8ZSqAItN0d1YAAM25Fj+YhNo4rkF20lijIrqnXSwuP8Dzk0xggoD9x6fpFXV6\nBjcQCIf17sFkY03sde2DC5aYCdz0A/7u+jvVP6YCgDjwgXNeCFf+BTx6M0f2PZDsbNQnAiP5s4X0\n4xDlhfIAxh6C4QuUo70xk/YjaD9ARfs5or52YLyWXnkQ1HjiN9tCZS1n8et9LwdrlwAiH4BlY3Ww\nM0Yx3L6lTEARAczoBC3ZrKTCQJvk1Eve8qA6RRiZMJ2vkRO4ZvcgO916R0ckSTeerScHasQmoCik\nr7d2EK//LO4NzyYXVfnc/S31WysAk6Catro2rz6XKkMNMNJziQpj1MXKmjpaYeNgL6CINLmMlmsy\nUJCq07TOqsamKzEBjKITlwI3Xgx+ENVpJh096OmBYv94lT/76n0Ugjnyxupp1dH9HJmuc/9+XZbB\nnVPk15iJr/mS6R/SLXQnPjK/CmimFEALAbTE3ve4o4hepQDOOf5t+PxV6ovj96vBIN/T5lSUOi/A\n694MXp3QdxmRg/j5XhjbHUeGAHDwtjgC6JFGS7mQ48lgdmSqTk4rgJ5SkSnZHUdYKQLoMghgti2y\nbG7iSMr0UZ9NzCV+Q5FemYZyRn/iBTC5n/ngBmFMRjL0GT2unonTPaQUuJln4DeQUtLQ1yxOFEUH\nyrfx1TfDf72b6ZqXLGvamFbE3koAXeugfzsA+0aS63LnEr+KlJKC7gOtKj4hgHkUgJRKAQyfD8U+\nZY40FYA2T1Y1AeQMBVC2O1yvV2vLlracTAEsDzIxAdkdZruhl1YAEUuP+ooQ2ghAqgciOtm2F4DX\nwQlcobujCUg4UU6Cu6ACKItkZjK67aVUKJH3K6r8w4/eC+e+BIbOBWGnwghdp0woBX6jki5+B1wb\nXgm5MvxMqYBocNi0TjnFQ4MAAuOYrS9ul6wpM1dLiGHoNwn1DDVWAL7LpCaAvkDNzuJZr+5Qt/zo\nm7zmnt+i259KHa8x/ijfuf8Ys63ZuCP3djbBtKxBbMI1nMBBKwEYdnebgFJzHKtvM01dQoR9P1a/\njz+g/C65Ylsk0YGf3wzArvwl2gmsCH6qfBaMPZRWS3MjeDOKAA4Hg/HH0/SkCWC6zkBRdd/uriKT\nsgfbr6lBy6u1KYDWKK9b7tmFZ6id+kwS8VOrqAGsTEOd8+hdycSiA1w/jAf5MPSZHtdKpWtdvCpf\nDL+p693o4IRwYRMqj96qFiO67yvw4NepNP3U+8/MkWQNimmDAHRwx8HjyXVVphKT1lzTj2fjfmQK\nG38EvEbiBJ6PACqj0JjmaP4MJoOiVgAmAah3slZXJOeIEMKAAxNVuq0O44VbRbb4QuxMASwXygmM\nZatFVloQxiYgNeDn8Qil4L4xvei7224CgnYCECewYabDQFUi2DTdHU1Awo6ykn381u8NH0AXSQd4\neOiXqMgi+bCmBj8Zwsv+HvS1m5EM0nKoiSKhmQmscf+UTe2iV8P9/wGVMTytkDYM9JG3LXxDkZiz\n5I423Ml9uM20fA48l9q0mo2NY/oA1P0p+4ocZvObopMAMLT/ei6z9nGOOJK+HVMHKeVsukSLTD96\nT1tkVsXuX5gADD9N0Cr7DRPQMNNYhIi+LbjC6KBePSEAu5AaDKSUHNt1CwfCDRyTg9oJ7ONjc9je\nDmO7U2QZNqtMHT/IjOxiLizEnz8kzlJ+Dn3siapLb0ErwXJREQSowSn0WhTAXJvp8q4HH0pVZI1W\n7wKoagLIiYDajDZHPax8TWNzTQ5NplWR6QMg8KlNax9G1yCydVEer86R6Xo8K87NRwBhoDJtP/sy\nFRN/9i9BZYxq06cLY3W8qYO42p/HzCFlUy/2gR5A3UoSHVebTghgcq4Z+wA8r6nu64cvx/vUi+OA\niU5RQFJKvn+TWkTmHTc2+dquiiJ808SofQANww/muw0OTdbjaMMU3KrKlTCQKYBlQGVUahOQcLA7\nOIFDPWuIwkBzKLv7/lldM8WttDmBoUOMethhtmkgFeccelCfYjLsWlABFHT8fQpGFFA0AzrS+xR2\nh2dQpUQhqCfOw+6N6rflpENghUNDFMGtxqFp8eGx+WHvVWr2fNdnYwVQLBY5c6icIqS23AaNw1Jn\npE7uw2/JkpV+k5oeZNxiYuefrHqU8zZOfRzsPG5Rz3qDJk0/YEdVrY3aK5LjNWUOe+4INdenTMvz\nGLmnTQE8UrxUEcA8xdd8gwDMv1Vjk8Fus9Czyd4tNEUx2ebY/arTb7hEDTx+kwPjVa7deYhb902w\nrbGbn8szmfIcFc4bNPFweCjYDLVxrOrR5Nrqs8xNHGVUDqRU4C7OVPd6XEWP1Jo+Jf11T5cyAQGJ\nc7xVAbT0AVEd5eBYYhMPZpI2NGqJqtq7V8Wr+/tv4T/vPsw/f+zDfPyf/4bDU8l9eeDITEwAc/Um\nXb7ev2sdsoMCGJlpxASwSUww/Y138Z93PqpX8UMl933+KqVmL/nv8Ls/gTOfC16VWmWWLhqxGfTh\nhx6IQyuZOQylAVX2QvfrfDNRjs0ZRQDTNZd3XpsEFARug8oxdZ254/dyTqActJ0I4Ae7RrnxZqXo\n7A0XMOZqkq6OJUXktAKo15N7dHBsGjcIycvkmKPod92rtuUqnVYKQAjxy0KIh4QQe4QQ7+zwvRBC\n/LP+/j4hxFNX4rzzIZD69RDKB9Bq7wY1IEESBprDR1o2VZ0ZjNsSBqoHZCtcmgJI+QCaarYw7nfF\nL3DqWJEPQAT4stUEVCdKFizT4LP+i/nKJf/KyGyDKkUKUjsPC73KDAFtSyIGwqYpSgiv2qYAAmy+\ndqgMZ18Jd34uTljJ5Yucvb4cr5wGajYfwyCAfaGevU/ua3Oshb5LY3YSX1o43ZoodBjoQDkPlTEo\nD2Pn9P33XXbt3c/54hCt2Cc3UayNUHeDRSmAn9sXqSicKEzTvO5QMjqdzNTCaDbYnFM/RmLPNqFn\nkL2b8UwF8KgaEBQBKBPQ2750N+/4j/v4h6/ezFYxjrv+MiaaevU5v4qHzZ01Ze7qnUoygN1aBTl7\njFHZnyKA++UO9Ycup1BzAwq2GjD7yiUmpK7XNHVA/c6V1LsAHRXAtkIlHc01c5TROXUvm9VkNjtz\nXN3/dWKWD17zHf669le8l4/w9i/diR+EfPeBY3zu1kfjPJPJSoNBoffvWte+spXf4KihAAD67/wX\n/uO6L/KvP9kHD39XZQwfuROu+ij8P5+EYi+U1b3yZ4/TJZp45c34WIzsTZzvcvogE2EP9x2ejgMq\nCm6iAPyKUqBfv/sI9x9MFE/oNTi2N8nwLulJRaeExHsPT3OedQRZ6OXCc89jzNd9rToGZf1eax9A\n0/DtPDKiM+ANxXNMagJwa23vrJM7TQhACGEDHwFeClwEXC2EuKhls5cC5+qfNwMfW+55F4Iq46Cq\ngSKcjgQQJcOEjs4DwEdaOTyrqAbnZgUhTB+AeiCtJqCOpW7Ntpjf19QLeNwrdlyw3Molkr+TDyBS\nAF00qFHECyUjMw0qUteYnzoA5WHjgOnO50sLzy5h+bU2Augvl/jpnnHcM6+EmUPkakpNCKfA2cPd\nNMPkVckfvAn2/0R9bxBAXRQ5xhBM7ot9LPF98D386gTTdNPbrSOt/CaTVVUGQnWgYeyIvIImx37+\n47Z7BPCI3EJ3c5S66yo7dYR158Dk3ras0zvkheqPwztpxd/esIuD40m8uz17mPB9O+D/bFU/3/vz\n+LutQjsUe7cQmtUaH71FvTPrL1QDj9/kWdPf4Af5P6Z3Sg1Q9eHLGGuoe1gIKvjS4dZZNWD0z5gE\nMEexOcasM6jWstB42N+kyOV4RAA+RU0ApXyecWud2jAKhW1xArf6AJ466MX9Ylz2cvzIXp79dz/k\nwHgVt54QQFT5FOD/PTexp18z+nK++4k/40+uvZcnbe2L1bLveQyg9y8NdlAADY7O1Cla6fY8y3oA\n+7/eBV/8dejZBG++EZ7yG8qUCdCtCCCYO0aZBrLYSyW/HmdyT3wM4VbYWyvw3m/tigMqSp6xMllV\ntV/u/wn3F9+YXKPXZPaIUYZDw+6g7neNzHJp/hhi+AJ6S3kmA933KqMq78YpQWOahhekSkDsOzah\n63wl13001MEQbrXt+ZxOCuAKYI+Ucp+U0gW+DFzVss1VwOelwm1AvxBi0wqcuw1NP+ArdxxCgEoE\ns2yVXNUKze4RAeTxkMLhwk191PUs2TQBzacATkQAqXK+OtRutJlnoLvYtq1JAKYJKMRSPoAg4Fes\n28iLgIos4gchIzN1VXAL1ODXvSE5YMuKWD42nt1FPqiTx6Mhk0HsaWcO0/RD7nfVY1k3pzMd7Tzn\nrO9OEVJp5GfwvXfpxiXXJ4TNIbERJvbGCiKCDFxkbYoZWaa/Ryfb+VoBdOVV3Hb3epy8ui/Sa2Af\nvLn9hgKH7O3YBNiVY2mH4NlXqt8tFRnvbm5W0TmHb1fEpRcr+cKtB/i3n+7nRResi7e1jt+H5dV4\nZMdr4Wm/nTrONjFKaBegNECXSN6D+t6bGM9vhkI3OAUCr8mTvbs42xrhFcV7VUmSDZdSCdX9LoYV\nPGwOy3WEuTJDlSSrdGp6knVymq7BzSmzWzW0kcMXxARQdQOKlvZXWTaNon7uE3pAbDEBtUYBnd1V\ni+3Rh+R6+qsHeL7cyZdvP4hnEEBXcxRf5KE0yFWDB1PHeP6xz2IJwUeufkocMGGLkGG7iiz0gpNP\nEyWA32BkukFvLm2O+z3nG7zJuYEvBC/m1iuvgeHz0vvpiY2sjFGiiZXvIjewjbPE0dRmU7JHldbQ\nJqAuPyEAofMkzjn81dQ+gecix/ckZjSNuK8fvhPG9+AFIbtG5jiLwzB8Ht0Fh7lo8lUdV/6fYh80\nZ/ng9x/h8Hhy7gPHp+lx0uPQMakJwKu2hYHm8qcPAWwBTJ1+WH+21G0AEEK8WQixUwixc2ysQzr8\nCWAJwd98c1ecCCbmMQFFVSulk0QBhZbDZdv6mAsLbXkAiQ9gaVFAgUkQOqRwwhUMlBcmAHPAbQjl\nWDzv+A18JP/PAEoBBJKR6QZVqY81uQ+6F1YAgdNFWdTJ46tkJo2Ltw3QXXD47qhy0G6o6VolTp4N\nvcV2k5SOSTdzLCzbYW+wATm5rz2LMnARjWnmRDddXarT7BmZZHS2qRSANgFFBOC5DbbM3s3hYstA\nANR6zwagXD2YWlOZs17Qtm0oBeP1ELnlqSpi5/OvhBvfx492j/Lu6x/ghReu578/eWO8fXFWhTu+\ne/xKwl96d+pY28QYbnkTCEG3ESNfCmvcXd/II8fnwClQq1e5AFWv6L8V7kQMncvg4FC8+lwprOqB\nUVDp2kafm1TdrIwfpiRcNmzennoHPGkjN1yiTEBSUmv6KtPZckAISl1dzNn9MQHMhTk1CFqOdlCm\nCSBfH+c3n67I/jAbOFcc4lP5f+SRO7+fUgAbmVLlubc/Ex75bvreOl187Defyrb+5L21CdharCP0\nkqfROzirB8rQUyag7ly6PVVngOp/+xxfGHwrb/7i/ew+1pKFrCc2VnWMsmhgFbrpWr+DrVY623dC\n9vDI8Uo8YStrAqjJAhumdhJ6TYJ6+tih36Brbj8Py60pU6cduuq9/PyvEtzwvzjvXd+mNn1clQMf\nvoDughPnDeHOKf9PUeUFjM41KJCMFYfGpjmnP92HjpsmoNZw8ifqegBSyk9IKS+XUl4+PDx84h1a\nkLMtfunC9QhUMThpdTYBxQkZWgFYQhIKhydvG6Aii9TmZlJhoHEUUKssPJEJyFQAOqKkKedRAE7y\nmWcSAAXlPDTOXaVIpekzUXUTBQBUcknoYKsPwMMmzHXRSw1LyBQB5HMFnnfeEF/bI5H5HjbXdaq6\nnaeUs9ujlqpjEPgpE9BgT5F9wXpEbZx8M22Gkb5Lzp2hZvfGSS4f/O4DHJttMFDKxSagfEFdy+HD\nBzlfHmB225XJgvMaQs8OB2ppm/7XDndB79a2a254IQ8556vBUQbU993CW794Fxdu6uVDr3lKHJII\n0O8ew5M2PxsvcOOh9LPdKsYIymrQLLckSR2RQ3zsxr1gFwgrk5yh/QVWfQI2P5UNvcV49bmCbFIs\nqEEznkHqv3trap60ccuOFOmGWPhDF0FtnHDuODUvoGCF8QDbV8oxYQ3FJqA3felBZT7R5SDa6mFV\nR9nWq/adyCVi/BXuDew7kky81gtVuoTtz0zqE73qc/Di99IbTPKsDWHKwWwTstGpqlBMiNs3o2fX\nXqPGyEyDbichgO8HT+EbL7qR8mWv5LO/fQVdBZs3fPoOjk4b91jb153aKGUaWMVuRN/WtlX7SkPb\ncYOQfVPq2XWHSg1+1P4NBppH+cKH302XTGepS99lvXeYsfzWuDowaHv9je9T/fboXXzM+QBvcHSh\nueEL6C46zMmkqOOcbxMWVF6A64dsLifv7dRclTP70xOyWAG41XYCsE+f9QCOAMaCqWzVny11mxXD\nSy7eiECFpwnLSc8SUbPCAh6Blcd2DFOL5fDkbf1UKVKdm24JA+1sAjqRAkhlyuqY8iY5BjsQQGz/\nhlTYZU0qBVCx+43PinEkRqwAgJ+OGI+0RQHYTg6ZKzMgFBHF2aiAk3P4pQs2MFpxqfWdw0Cg7b12\ngVLebo9KkiFUx7AMBTDc28URSw0mg9W96e0Dj4I3g5vrxYqc3VEkSKGh7qNBAI2Hf4QtJIMXX0mF\n5PpqskDvxrMA6K+kCeCvfnCMxvClqc9CYfOkrX18cv9Q/Fl+4kE2FHz+7beeTrngtHW+ETnIYE8X\nn7ppH3/Z+zfcGyrFsU2MEfRoApDpUMgxsY7/vOcotdCmr7oPy/AfsfkpbOgtUDcGF8vJs6W/xEyQ\nPIOa0xc7mkuDW1I+AF9auEPKteYevQ8pVakLkwCOMxgXr6vLvIqqiesBJQNu6BRVcpVXAyuHLCYJ\nZy+zb6dcT0o3FISvjrH9F5Lr6dsKG/V9Pn5/6v5ZhMoJrAkgWtt2Ws+UG406x2YbdNlJe6bpYfuQ\n+n5zf4nP/vYVVJs+b/jM7czUdf+yc1AaJN+YoCxcRK6s2tGCbWeoZ/XgqDLx9moC2DVwJTcHF3PV\n7L9zXjGtAIK5MdYxQ9em8+P1QQBKQQXu/AyUBrAbU/yyfQd/6HxVmXm2Pp2egqNqQmncf6zBqJuH\nxgyB12BIJOfJ4bOjPz3cHicxAbWVLj+NFMAdwLlCiDOFEHngNcD1LdtcD7xeRwM9E5iRUo60Hmil\n8LJLN7F9sER/VwE6KIAQQQGXwCpg28ktkCLHWUNlmlaJZm22JRFMddRWx5BYihNYE0BD5hnsaV8c\n3M4nL585466TV2npxmBbpcihSZ3N7CSVRSdJSKLV0XzRlkHId9NHei0EAMvO84IL1mMJOCSTwRI7\nRylntzulgWB2JC4ypo7hsG67crgONVuidwKXrmCOoNAfE0AUhz1sa5ND93pymgA2TdyGh8OGi57D\nnNHJahQZWreOaVlmqH5AfZgrIxHMUuYOd3v6tNj8+csu5AeVM9T/UmAj+dxLLDb2aWJpJQBrA7/z\n7DO5ec8EXxg7i8/5L1LXJ2QcYvtIMU00Z511LpaAPZNGZE2k6DY/hd5ijoZBuNg5zhouM+kZE5Di\ngBpwgXz/RkJDwQVY1AcuUH8fVY7lvAhjlddXynFUJuqvQZ6qG6hIILeS9gEM7AAkzI2AnafZpUjt\nhqHfIY/PS63b48RHAKvYC5suUzZugN7NKuIJVA0k4x1wCOkJZxMFoGeyUZXdyZkZglBSMghgSnZz\nxrrkHb5wUy//+rqnsX+8yu9+YSdNXx2/kh/Cmz6i/D75MvSZc0qFc85RtvmfH1MmyH6pBuF/+M3n\ncMHrP0C/nKXfTQ89fXPK3Lnl7EvVZEvDJlDX/NL3p0/y3D+BUj89xRxViqrgJGqSOC27oDnL74+8\ni19rJr6GPB7be9JKdkz2q4oAbq29XM3pUgtISukDbwW+C+wCrpFSPiCEeIsQ4i16sxuAfcAe4JPA\n7y/3vAsh71g8aUsvhZwDHZzAigA8QqeIY9zo0HKwLIFT7NE+gA5O4DYfwMJhoGHgx51JRiYgcgx1\nUACR/RtU9dEIlbAAMsQ2EoyqssjRGUUAff0D8edxMTVoMwE5Tg6rUI5np2Yyk+04DJbzPHX7APtn\njRfVKVDIWe2JacB3b7s7pQBCYfOkSy9Tx2tRXXbQpJsqsjSA0CFusRlO176nPEyhqO7BgJzmYPF8\nRL6cktkNUWBjb5GjcojtoXZKbn4KYvgCXnjRJr50OHHoggp9fcZZ63jGxedwT3g214XPQwqbbTN3\nJhvpZziiB9Bqbh2vvWI7pZytFnUyyM8qKsfqV9b/EVc2/yH+vGfDGfza07amCEBsukyR8MZLKeXt\nlAKQVo6zh7sZaybPudiXPDvRs5GcEQkSYNPI9anqk9oRnG8xAR3yE/KvU2BsrhmvCWASgDWwQ/0x\ncxjsHAc2vJiXNf+We856M43Nz6QgfMZIVIFd6lVRNVuepq6ne4NacN4uKF+QYQKyCCl604YJSL37\njZw63pReZrFkRAG97BkXs6U/PSF61jlD/MOrLuO2fZP8ybX34QUhP54cYIu7X4Vp5svqXrSgb/0Z\nXLy5l3tHlELrpUqIxUB/P+vOfQZc+qq2fbYHarKy6exLId+yTsez/yffrJ4f/9t8y8/gWW8DoLvo\nAALPUeYtlxwzQQkaM1zauDN1mJwI2NKdJoBZ2YXvlMCrpSZS5n1bbayID0BKeYOU8jwp5dlSyvfq\nzz4upfy4/ltKKf9Af3+plLI9Hm+loReFFx1uZIhFQXhIu4CVUgCqMxW7+yhTT0Xqx07gFpPPiWqZ\nhKGPh00gRcoEtK67kwIwTUDJoBOZapwgMTvUKMR5TT2Dala6K9zOXc5lyQFbszAtB7uYrLfrWcn5\norCzlz9pE0dqxn7aB+B3KF99yz33xzVgACQWv3jJjtRMNELRU3HQdtdgbOr6m9xneNvAz3jRdn2n\ny8MUisl9mV3/dADmDB+HK4ps6CtyRK6LC8jxi++E37uZ33n2mdxW367utUZkRnnnSy/k6uA9XLf5\nHYitl8O+HyWN0wTw155a39UrrqOvK8fVV2ynu+DQ05WcP3pGdqHIPrk5/tzq28LrnrmDRqjuk4uj\nBpvLXgP5LgqORVOkFcDZ67uZCRJSGFinndF2AYr95HLJuxtgqWUDN1yMPfYgADlLxiqvr5Rjt5dE\ngNVl3iCAFh9Av1JDzBwBO89wb5EH5Q6GuwsUf+FNANTs3rjooFPS+QRPfi1cdJV6r4RQoZnVsVSV\nzTINVZJCO4Gj9zgoKAKY0QSQF4FSIuX1bHnub9EJVz15C+986QV8496j/M5n72BXeAbbrTFKRAqg\n3QQk+rZwyZY+HjxWQepcAM8uJeGkV/4FbHxSap+C8Aiw6N10LsUuNZg/GJ7BrtzFuFf8Pn/67aN8\nL3ga/1v8HoWNF8TH6i6oZ13PqQlYE4dxv9i+LjAqyMT0CQDM0oVrlZSP4TT2ATw+oauBdrqRIZaa\nfToFHMMHEKWt9/b2UxbNFgWgOmObCegECkAGPgGW6gi6jK0n8vT3tCuA3DxRQPG6xX7ivIrMU/1d\nOTTyvhYAACAASURBVHLlAZ7T/CC/4v4tNbM5rUk4lo1TSkLdfMuQu/o+vOrybSmTEnaeYicnMHBm\noYJjqKtQWAx1F5jMt3fMLldFa+R61qUqHb5xw8NxpAbd6ykVkxlYqDtqpADmKONaJa0AjJl+oRss\nmyvOHGTzlq282v0Lbg/VrC2qRXPmUJmPvu6ZvOeVl6looSN3JQuo6Gd4Y3gZV7t/zi1bVYz4n73s\nAr7/9uezYSC5Z06+nbgBcv2b2TJQiicKFdENV7wJXqlWahNCIJ3k2oSd4+zhcqwKPHLqOkDNsIXA\nyZsKwMLVBFCY2sPbnWvYvu8r8TPuLeW4JUjSbxoUGK80MdcEiBEpgLmjYOcZ6lZtGO4pwIW/Cl1D\nbBweYrdUJhZR1ATw1NfBqz6THKc8rNSbQS6bc0kSGKjoJQCRL9OUDnMV1Qfy+MqM9I5HoL/dlBPh\nd593Fq//hTO46ZHxuD3qAGVli8/3pHco9HLJll4aXkho6XIQjhHeOXAGvOWmtvOMOxvAKbBxSLV7\nd9+zeWf/+9k54lJ1A97s/TE/7HpJap+eorr300WlRFxyjLoFCNyUeRVUZdqhfHrscK2iKkfvKgUQ\nmn3sdFIAj1+oMNBOUARQxLKSWxDFLJd7+rUCMDqNnk1YsoUAOpSaNuG6qrBbgJ2U2e0qx+v7mnDm\nUwDRusWB2v8bwTN5SJwJwKa+EnlHcFiuJ8TizkeneNE/3UjDC9qTzewc+Wg2R5oAHF17pFxwePbF\nO1LXnWupBRThFWcJHIMkC9qHYQ+d3bZtb6AUQKl3XZLtCwTrztUmIAGlQYqlZIAtbr4YgKatCOmb\nA6/jB/2/RrngMGEbpZK1LVgIwf94zpnslBfEi+aExn18wQXruXBTr84XkGpRbogjuXxsbg0vpm9Q\nmWJytvITFAuGs1wTQKVlkZnucje9RQdPqPtYt1oGJlDJWRHsPOcMd8cOfCmEGtQAetRMPpdrIQA/\nhL5tCOnzCutW9YUmgP6ufFIPCOU3SikA0yQ3oBVAqBYfTxGAk4df/xxjT/9Tdofan5JPx8cnF71B\n5W8Y5osnD+j+EROAmvVa+TJN8lRrVXoKjqrPtQg7txCCd7/iYl59+TaOlc5JvjjnRWqC16oChOCS\nzUpteJqMfbt9+VVy6l43dd+qlNU9iSLxbCdP0wu48aEkIioVlQQUHIucLRjPKSXoSoejzYI+bjqO\nf2OPjT1yFwibG3/p63xo6N30lfI0KCoTkPRTBRdPGx/A4xZaAXRaWMEmoICLlStiGwQRlTwulnsp\ni2ZS4ArixBK7tWjTAiagn+2bYHS6SoiNj4XQERrlchmrdXYOqYExpQD0IJHXBPAe77co5tV1be4r\nkrPTj/GR0Qq7RmY7KACHgqEAAscwbRjmhkvPNDqVJj7Zob3rmeLSTUnn2tSvOtWGM1sTwYnj5rv6\nh1Np7o4I1SDStQ5sh1IxuQeD2qH87EsUobzotW/nVW/4nwDUu5S5ZCa/IUnBB37l0s28+KIN8Wwq\n7JBxzZanKefo3h+q//UAFt3zSzb3pjYvFhJiFjl1z+b0Or67QkU+PcUcQoh4AKk77QRgGfZly84x\n3FOIExEtwmSg1THvTi7tA3D9MB5Yt0dlKQwnMMDXg2cByseQNgEZ73J5OCEjO89zzhni9b9wBk/d\nrn1JO56D3P4M9kYmrpY6+jG62xVAt6dVVRQFpO+tU1DqSLp1NvUXVb2m1gVv5oFtCd73a0/ig296\nOa60+VFwGWzQ71hEAPnu+JxnDXdTytnUtR8tyLUvvxqRbd1S90EOanLRFgNh53CDkB8/NMZl25Rv\nZVNfWv0JIeguOBy3dWSY0FFAQJF0HsymslDv27YreP5zX8AfvvXt9BYd6hS1kz5ITVba+u4qYe0S\ngJEI1gqbkILwELliKgoIbS7Id6kZRFkkTlehB+dWE5A1jwIIQsl7vvEgPXlBsVhIhfT1dJex7A4D\nk9M5EziKH89rH4CHTTmvvt/YgQAAdo3MQavKEDaFcjK4STsZ2Byz+mDBGLz0MWTLQDpb2ABzI+RM\nktTbDm5V0SqtMhigf2CYnJMcKx82VRalTvXvyifXvb5ftbW3X3XsocFB1mvTmdetBt57Nl+dOn7e\nsfjX1z0tNlm1lSMG1cnPfB7s/ZGaKGgTULTPs84ZSm1eKhrmOv2MIgXwCve9nN/4bGwOiHwEKTOa\nRi5fiIlJ2IowNmiTgy2DZFDWBJBvVQBBQgB2FGaqI1C2D6p93+79Ph+84scMliMF0AtejZz5nuZK\nSckQO09fV46/uuoSSnkj2zvvcEjqbSrzJGSW16tnZ0a6RbkCup2RiTRfKNIkR0F4bO4vqX2WOMs9\nY6ibpzQ/we/LP00+7NsKCPhf++DtqpyDbQku2txLxdf+h1wHNabfcant+V2btKM3Mr3YeUamGzx0\nfI6XXbKRT7/hcv79jc9oO0x30eGoDn3eKCbjxLDWhV/O7aqoOlVRtjqKtCuyoBPBgkwBrCikBEFH\nH4AjQgq42Lkilt3uA7AK7Z1XxAqghQDm8QF85Y5D7BqZ5clbexAiiaIJpaCv3J0mngjGjMhMAkpM\nQHodVeGoAmqouOlOBPDgyEzHWUSpnER3hIYCMCNOOkl+2WKTnO06U0WAmAooeoEHVZx+2GqfBfrX\nbcCxLJ7b/ADTsqzWi62MxrP4LmMQsi3tNHvK6+DlH0x1irnhp/KS5t+xe8fr2s4horWgSZuAUjhb\n1TxiYq+6BmEDaedehC5DlURKcK4ZmY0cmuRjAohLWTjtvoJSwYlJUej7/brnKzOXQBomIKVu8q0+\nAEMBxNBVbc8ajkxeFgP9Awx3FxiLfABAN0byU64rKRkyz0DTlbP5aXgp1/rPgxf9747b0L1Bzf7N\ntXej96EUVXVV/xcLBZoyRwFPzaSXoAAi5B2Lv/zvV3Dd7z83+fDSV8Gz3qqI2ZhAXbK5l3qonr3s\nZMK6+kvwlNdxLL8DgKEztKLQbRJ2jrqn1Msvnr+eKy/YwLbBdlNSdyHHQanu5SYxmUrs80RehYwC\nzxP3ADJFABdt7mW0YSPdKpZsIYDMB7BcSBAW9jze9JI2ATnGTDw2cxTaBy6R62wCsjsogJmaxz98\n7yGuOHOQrX15QuHEZQCa5FjXU0B0knjGZ2kTkI6b1wRw7e89l006hn1TX5G804EAjs62+wBCn5xh\nAsIxo4BMBdChw7QoqUrvWWq2Zy6MHm0zqPwTfq79OKWeQfKO4JDcoBcxqessYKUACo7F33u/zm+6\nf5bstO5suDxdl2djX4GH5Ha6Cp2fb6RYOpqAAM7WZSP2/jC2hf9/L7uAL73pme1t7qAAXn15ZPpx\nEIJYkeW1uUjm2gmgK2/H2ddR1JWVNyYb0d9aDUUEoKKaRGcC0KHF5iRgfU+Bdd15tdymHvx6TAJw\nCvE55huES3kblxzv8N+iFhfqhKjsyNzR9u9Kypx07pC6H9uG+2iSp4DH5r6lmYBMvPrp27nINNHt\neDa8+G/atrt4c1/skJf5Diag4fPhqg9jF9Sgnt+gS45EJiDdHzb1FTlvwzw+EKCv5LDHU8/kAFuS\n0hDA3Rt/DX7hDwBwDt2mnNabnxJ//+xzhpgN87j1OYT00yo7UwDLRBQGOs+NLIumMgGZZpJoAO7w\nwsTOIaOeN3Q2AX3wBw8zXXN59ysuQoQe0rKp6GSmJjmCUGJ3MgEZHcLr4ATOh4oALty6DkfPjjf2\nFcnb7aWldx+bax/8ZJCe3RuDlJM37tMiFECzV83ymTOSasz7t/1ZzAxcnNqnQhlsB0ff8zoFREwA\najARQvDR4JX8NEwnWrViY696HqV8ZwIQkQLoZAICpVIGdmgCCMByePPzzuYXzl7Xtmm5ZBCAvmd/\n8IJz2PPel7Kpr0h3QeWPABQ0AYhc+2yxlLOpRVVlI8XVkQC0AtAmoGgyoExALSG2zSTbdFCrwvW9\nBXqLOWYbXjyZ6TMJwMoZJqDO/aOgJxW/8qQFajZq0jbXKgag2B8PpFv71O+B7i48K08B96RNQEvB\njqFyHLnXaUIX4dzN61TCXlRCRL/nOf08f/H8YYRo718RNvQWOVyBd/R/gI8P/3kqZyV0upI+LQM4\n8/mpidSzzh6iRoGgGSkA413NfADLhHYCi3kUQFk0wSlhG/bouHRthwEwytJtXVymVQE8cnyOz9/6\nKH90aZOLb/5DeODreLm+OJa9SU5ZpjpFJxkdwk/5ALQCCOtqIRnLjmd8m/vaTUCXbOml5gaMV1vI\nKfRTA440Sk+kTECdOkwLAQRRhzET40zC+Z1vc+D8N6X2qeo1iaP21igo84FbSRWxu/qKbXzg1Zex\nEDZoAjBNRiZOqABAyfEDN+mSCPNvlyIArQCEEDi2RV8pR28xuTd9Ob2cYIdJRCnvxDkdsdPdfNeG\nL1QD0UaVZVvQ0UeR38ALQrBzNOzOM9Kn71Cz7nXlAr2lHLP1hABKRvVSSgOJCchp99NE13fnu17I\nB379yR2/BxIVMduiAEyVEpVCsXL4okBBeEt2Ap8Mtg2WcKNlXBcgALHpMsS5L0r8ZboPRhnZzz9v\n/Xy7Auo9PD7b4E7/LPoGhwkLho8tV05fo2H+AUXYXeVeLL+GJYP06mmZAlgulBPYmtcE1ACnkI4C\niv7uSADtcftAar1hKSVfvu4aPpP/e9728G/Dnh/Ac/6Im5/+L3HNfmn/3/bOPEyuqzrwv/OWWrpb\n1ZJastSyNluSFzk2WNYQ2QZjkGzABgzYw5DY4AyLwaz+bBjMQAwBJwOZwGQYYIIZZoYvgXxJgBmc\nDAOD7XjC6kxYYhaBDQFig7HBeJcsqavu/PHufXWr6r1auqrVtZzf9/XXtdx679233HPPcs8pcvV5\nJzYsQEvxpP6RjIVgxeqBdDYYh3UNoFkAvPTsxARz98NNEUq1aqMACOsaQEO0VEb/mwVpUMmYGTY5\nncNSsp1HbRTT41Gl4dgPmiI8mGTNTGeTwL97wWk8//TWtQQ+J62vUAgDtsxlhPhB6hxtKUnos+3p\nifD56Vfb2lxXTPkCoPE+WD9brqeUACq26LczLfhMxWHq0I9SDcBrt2Y7XP3dNLKlaBPGuWv+wGPJ\nth8JGqOUHO994RP50KW72LpmmtlyzMMHFzDe4PfjuXPgHQ8loZ4zdSdwHnMzxUzzYspMjgbQIACs\n4AljFoIim+U+ttTutma3pRMAx6wo1RdvlvIFAE+5Bv7Vn9Xf22NaWRQqpYizt7dqhI37KXJoocZd\nDxxgthyzorIyFdgmnmocyJ3Z0f/93GpK5hCxNJmA1AfQJ23CQAFKHIYoGTzTbJNuAM4oxhBl2HTB\nagTGwJ038eAH9/G7913Nk+KfJCsOr/o27Hs71fJcmrFzenqa2amYMJCGFasAiKTRP40LwZIBplg7\nQNV+Xy6ErJlJFmnF9iHdOjfFHdc/iwtPmycKhLsebErJbGpNGoDXJ3/wzvKB2PP4gYWLeP3h1xDO\nZgiAptl2beVxvPLwVXy2mkRPHCkkDmgnsA5SrJex9AvZdMHmuSn2v+uZnLJhNrtB4DSANqr01qck\nx/zL/W1V7hlvJXDzjPmdzz2FD11aL3Dnin5HGQLATweRpv7Osk9bSlbrrCHsnK/w0S/9mMePVPlV\nLXtAmylGXHBqcl0q5YjD1RqHgvr2xa8P4QRuPzPNYsWmg2hK6+ULAOczC2M+N/0cpjnIhj/f1/++\nOxAGkqZvCdsJgJYfJsd02oZpvvKWvawotT9Gp4keqRoqpZj5leXU3CvFGbsYtQCrt9UX4Hkce0wS\n/DDDwcbiOboSuF+sBhC1OZFRkTCQen1eNwhkDAZxMVsDiDkCNzwVPn4xR+7/MR8svoLwmu/AOUnC\nKEhuRqcB1Gz6hVAkc3WtCxfNWghWMgdYsIPsq566jQ/+djLwOB9AKQ4pRAHFKGT7MTP89IGMvEVh\nnC5WMlF2n8gQds5p/fXaCdxYO5vi7LpWJ3PTbLsYB3y+9iQO2YU4tVJyPiJ7vH7mxYY6Bl2SRgll\n4GZTLRWpfMorkzUB0F4AlPM1gFXThXQQAChsSkwmha1PatnOVCFME8JFzgSUFaNuKZXqPoC3Pftk\nfvbgQT78f/+JXxzJ0Xo83LqAh71MsQ3Xq4MTuCtcOoh2GsCWs5P/c9vZP7OHfxm9Hznl+fYY1rGU\nOA0gLOdMErII6ilfmqPBsvCv/abVZdZVSjzkIoGccJ9eCyc+K/P3G60AWCEHG7XVo6QBHB0xsxxY\nDSBsN8uISkRhMhBH1OoqWMbJj4qtg+LDppwUKz/0KLeceB2v/Mft/NffPou41GhCCQNJfQDGziCD\nQJJMgE1J06oSgTnEES8ZnIsCis0RHpPk4d8yN51mUHRqetFT13duqPDTO5o0ABuyuhBOES88lNZC\naCHD6eWiIpzQmioVkgfYjwBpGkTd8UhUhCoENjSw4DQAPztmjxpAR4IufACQmIHu/vu2My5nigFa\nBEAzx51zKfdv+02OPXZ7y3dTngYQRZ01gLKddNQIOGvbGp5xyjref8udvCdcQTWIWyLSfJwAeORI\nQGpc87W8QQgASK6bq0Lm8B3Vv/kqOOnZsHITW1bfTiHaChd/BPa9PXV2LxXOCRyXs01mmbjxojnp\nYw7HrKjfG7s2r+KeBx9PciiJF07+ilsSx3gGLiqvwmMY8Z5H9QH0iamBBLk+AMBqAEG9QLtrm/Gb\nQoYP4E+r5/Hq6J3c+5Iv8tr9p3DuzmN5yo7WgSyUugbgZmGheJqHx4K0moAOesvKsxY2OZNK0XNo\n75yvcP+BxqpLTgCU3WKw5syHbXAmIGeimi5EacoCr1HDW3c8LuQxnE6clFFqAvLO6XR7Z1uvuMiN\nrBXMDTjHXLt2/oSggwAAmMsY/CHR0Ny1LLnQ0hwnLEC52BgF9G8vOJlA4KbqLh7c0ZrV0sc5ph86\nXL/HGhZFDsIEBMkk4FBT9S5fAxBJc/1c//zf4CMvsRrX7MYlN3NsWpsMuoWpHgTA6S+GY06B3S/t\nqvkxlfr1O2HdCtbNltL05eLCqVeshzjnvrETgFQDaDMJXQrGVwBYE1DeOgAg8QEEUk/CJPkmoHKx\nkCa2cjxgVvA1s5P3/J87Waga3nbhyZm7CQJJfQCBOZJ+lmkCyhQA2XUCHKkAiD0NYL7S2tblbLE3\nnXQxmDnceawaqwEUw6R4t0+TCWjT6jJnbZtj/erEBltcMWePt8kEVKzkPyCLJejCBAT1tBBtBYD3\nXZsBuxNTXhTQ6oqdHTptK8PxXramJ3cdt8xN8/KnHM/fRWdSesF/arsvpwE86Ect+wK6OGPPe/eT\ngEx8053bfvNaBUscBg2TlKVm97bk/oynejABVebh1V/JzDSahb9yPQyE+UopzaIaZq2nacaaACsc\nSMyszk9zlHwAY28CCqJ2JqBmH0C+9C0VYxYIG6qL1Qh48MBhPv2Nn3Hludsailo07MYTAC5stGG/\nHrUMJ/ACIUeIiTmSqQEUMjSAk+crrUVcXD6YwnSSGrrdudm2t2GAdxk83TYLYZCuWE1pKkI/VYj4\nxCv28KNPfx7ugdnVyawzbjYBTTemXhgE4nwA7aKAIHnQTn5Oqx27uY2j0/baMFUI+bUVeqEvSC7/\na1h1XGt7uwLZCV2AN51/Ii89+7ikktnLb8k1IVXKTgOofybNqUFe9PHM/faEr7mFBVg4mCsAjjap\no72bgbgP3nrByWy3i8XWz5b4AU4A5Jv3UqwWvkIOYmbK8Ii9RkdpHcD4CgAApCHd88sPX8Msj/He\nwp8kH8RlorA+EKerczPU4lIcc4QQ32q+QEDNJHbA1zwtW+2HZLbvFoi45HFRIBzKEADVIIJqEvlR\nJaleVUM4LDGxOZJGAflkaQCrpgtJ4XnfTGxTNFCYhrCYvRjN8eJPN7x1gtQJABHpqAE4jl+XmH6m\nV9azbIKn2QzY/JMcS3KeOpqAAJ7z/ky/R31bg1HHkyggK/R8oXLcOZnt3UIwX5MLAkmydgJsPCN3\nX6kG8LhnBmz2h+Tstyd8R240XAIgrWCWl810QLzinOPT1+sqJf6ffdbjchfRR04bxyRm1rNeB1/8\no/qxLzHjawLK0ABqSGNlqyYfgGkTBTRVjFpm1PViIye1jRgIpe4EdgIgyIkCcmGLNQJqxuUPCjhs\nB45qhlPTmVRKTeq1Kzt5mAgu+xTsfXvyRWEGokJDUrZOpGkJ/HPQrAHkDLbiZrs2PYCL3nHhrYuJ\nAOpEOtvtRgCEUfuZ/YBmY8aYNCVIN0LF+V2qefmM2lCxuYkefrya5sWXdgJ/sfjXzjmUh0UAOBPn\nEmsAPnPTBR6TZFBvSLuShx8FFoSw93eTtRpqAuoX6wNoEgANRReiEpHnA5AcAbBgAsqF1qpYO9av\n5KqTd/C8J7aWpvPxw0BdBbEwaDoWS9WGaCYaQJCYnCRIQ9qy4trdOgBfAwAopYN2BNv31b9INYDu\nL/9Jx66G/fCJVz6ZB2astuM0gCBKHMx5ETdOoyrXS1dunZvi2ccfD99m8BFA1B2eHX0A3TCgiIxy\nIfI0gC6ib+x9GLYLZc4hCgOmCyEPHTyCCWOoHW5cBzAoGkxAVrg1p6tYLk66MKmlXezBCdwnQSDc\nVj4Hc6DGs7uJPvIDMY6S2cdnfAWAMRAEjWmOaZp1R8U0Jh3wooAaH/gaQjkOG1bnAqxfNcPv7Duh\n46GEvhM41QDIFABpzh0J0u+nSgUet8va2/kAmjUAl0qgZQZ5wjNhxfr2PoAmXKqI2ekys2tczhqX\nTiDJaZ47i157crIQxnOs3fqmp8H3D1gBMHgTUCoABvFQtTMP9cA5O9aw6cknwW10N8Ozx75l7eIG\nsNlynAgAe0/lFUfqixlfAMSJHygn5PGos25nvW7AUeTAqhN578PHcHHcxfn2fTjLIADG2ARUs+sA\n6ie11iIAEg0grfyVowHUCJgqRA0pmpN23T1QYSBpmlix6aQlJwy0ZvctQejF3Mc87opbZAmAHA2g\nbOPXW8xGp14C51/fkAm1cyfcufF+s2pLMrtyNWbzZphbzoTXf6N1hbGLQFkKJ7A9ziUZ9BaJiHD8\nvNV2uvEr2IlIZt6oLqiUk4Rw6aRiyQVAIdHyMqrdTRIuUWGxXRoNR6wCYImwBWFC3wQUNM6GoyJR\nEBCkAsB+5834FkwyE09MQI0PUNs1Bn47ER6zGkCtVDeDmCwBYE1AgeebmCoWUw2guTAL+OsAmkxA\nRWdOyn7wo25mKI4ww3RRmoU33pFE0UDvN3BT+uNBkgqApTB79MP8E2DdqW3r4KakUWmLGxgqVgOo\nBv0Jkra4dBAAW86CE7JXvE4SbnVwsZvnK4zqz9QyTFbG2wQk0vDwZGkAoacBZOXo/1ztSfzIbOCS\nQsgjzaerywczDIQDlHjLkZdx9cWvwlm8s5zApBpARLWafD9dilMfQPZCsHoqCJ8pu5J0Icc2H/Xi\naDrxQnjGI63x0XHZ05x6vIE37IK91yX1XQdMXQMYMgGwbidc+aXu2vY5c58tx9z16wOp32gxvoSO\nuHQQD90Fe65M8uxPOGdum+Obdz1AudsJVmEaDh5WDWCwJBqA//CYLCdwKEk9VlozXgLcVjuJ/7Bw\nCYUwaPEBZBZ1ycDl7v/z6l7C1Vu948n3AYRh3QQ0XSymOWSynMCFHA2gbDUAP4684bh6GRCm55Li\nFln28FRz6nGgCqMkG2MPK5K7xV2bdrnch542UWndUCklKaFdYEFmFbpB4DS4Xq//mHLeznX8j1ef\n3TZXVQPODDRqAkBEVovIF0TkTvt/VUabTSLytyLyPRH5roi8oZ99do3TAKRRADQ7gcNAPBNQ6wVw\nZphCFLREAXUbRRN4g5DvdM40AQWtJqCZcrFtFNCamSKX7dnckobCFVhvFlzpsfTgBG5LaqoYngHA\npdseOg2gF9z9uEgzlnMCO62xl6ivnnBO/FE+18uJmwCNmgAArgVuNsbsAG6275tZAK4xxuwE9gCv\nEZGj4Jp3GoBnAjLNAqBM7PkAsqqHTdlZdDFq1QC6jdX1ZwKx95DUsh5sV5LO1wA8E1CWAAgC4frn\nncr2YxrjjqdcLpkcDSAeVFx4OlANjwCI3OLuIRJKPRMEyeC/yIFhthzz2OEqC6kGsEQDjFsLMETX\nf6RwvrAR9AFcBJxrX38MuBV4s9/AGHMPcI99/YiI7AeOBb7X577bk+MDwDRpAEYg9QH4FyD5/LVP\n38HT5vdQCIOWKKBuncC+5h03aABZPgCnAYRplFCiAVgTUA+Dgatk1ZzDyBHFAxoQFusDWELcaR6Y\nCeicN8GaZbBvBx0WqbWhUk6uyyFbHL3tyu9+SDWA4bn+I8UymoD63eM6O8AD/AJom+BbRLYCp5NE\nQi8tNhtoowAIMM7cA4kPoIqnAXinQwIwVSrlYlonttkBm1dushm/7rCvDWStA3Chf3EYpt/PlAoc\nMvkaQB7TNp/84TwNYFCJuZwmM0QDgBO6A4sCevrbBrOdXgmivjQAgMdryTnoyefT047sQsi89OJK\ne5bRBNRxjyJyE5CVuPut/htjjBERk9HObWcG+BRwlTHm4TbtrgCuANi8eXOnw2tDqxP4Tc88iVXT\nBfgbEnU1jAhNNXUCN8RmBxFUqw32VycAHjTTrJTHqJa7i18PvVmoPyOtiUDzGbMCIIrjxHkrsGKq\nyCNtTEB5uGRiCzmWvjgelA9g+ExAqQYw6nbpIF70eXUpoQ/aaLIlMwGd9qIkqdz0kKSAGDUKQ6wB\nGGP25X0nIveKyLwx5h4RmQfuy2kXkwz+HzfGfDqrjbe/G4AbAHbv3p0rUDqSYQI6deMqZlyJN5sn\nJA4CAiu3Av8CBGFSq0V8m33yIH63tpWrj1zJdSu7MwnkjUGZJiAbE1yI6iagFaUiv7ICoJeVrTNl\nuxAsxwkcj7ETOHLXdJSjgCA5p4sNA52yGoBNYLtk/pDCVGa9W6VLRjUKCLgRuNy+vhz4THMDtr4s\nfgAAEBBJREFUSaa8HwX2G2Pe1+f+eqDVCSyB996rzJXi20jdrKthxu4StQn3srrrMK+8dlkCwDmi\nC3FsE8IJlXLdCdxLbpvpcmNR8WYGZgIaQg3ACYDR1wAW7wNwJqCDC25bI34uxpXUBHT0n59+74h3\nA+eJyJ3APvseEdkgIp+1bc4GXgw8XUS+Zf8u6HO/nTG0aACBX3EnoxhKQwF5N/P3NQBrInLhmb5D\ntx25AiDDPu2ylxbjmMQ4JawoxRwyvTuBi7GLAsq+sQZmEpDh0wDSZKCjPuiFcV/rAAAOLDh72PBc\nH8VjmE1A7TDG3A/szfj858AF9vWXICPgfclp9QEEvjqdUdlJsgp/NJiA6qmaoX1Rcp8wxwyRtQ5g\n05qV8APYumaG2g8DqgSUCwELNqVvT8nNbNtSMSfz5KAcpENoAnLnfOhSQfTK1GooLy67ptMA0tDn\nUT8X48oIRwENLxk+AAmCthpApgDwBmk3+NZSDaC7BypPUGQVLI/srD2KkyigGgGBCLUwOV4jPdjt\nbR+esCXHWT2oGWGay+To1DHthkgSx/5IrwMAuPRTSbqNRVCKA+LQW/0+6udiXBnmKKCRxWYD9W96\n8d9n1KCVTBNQqwCIo5CwKmnSp04EuT6ArLQKdh9hZOsXCFEQJBrLQo8agLjwv5yBeVADwva98Mz3\nwNqTBrO9AZBqAN0uxx9WVrSNrG6LiDBbjqkeUg1gqBnhhWBDTKsTOGwwAWX4APzBVVpNQG6GO1Us\ncPu15yd1WbsgyvUBZFxwO5uOoogqiQkoCEDiEiz05gNIU2Hk/WZQA0JhGva8ajDbGhBTBZtJtTDG\nt3gXVBoEgGoAQ8kIRwENLx1NQFk+AH8dQKsASGffEnQ9+EN+KGKmBuDWAUSRXbiWaABpWcVeb5J2\nC4nGeEa4biYRpHMz3Wlp40qlFNeTAaoJaDgZ4VxAQ4zVALxBTqS9BtCyEjj5UX2LLgqox9jyXqKA\n3E2QCIAkd1EYCIG1A/dc4SpopwGMuHmkLXYJyRgLuW6YLceeE3icr/cIs4xRQOP7dKTZQKW+EEra\nawBBlOEEbjABue97O235UUD5C8HiKLRhoIkACAtWYPXqaO0jlcBIY5wAmOxBb7YceylHJvtcDC3x\n8vkAxlcAOA0AL9rGNwll+gB8J3CGAAidBtDbact1AmdmA7W5gKI4rV+QCIBFagASdM5auufVvW1z\nFDA2vceEawCVclTXANw5UYYLjQJaAoxJH/6ahN7CMPswdLsOwJ812dl5ryagXDIFgKcBmICaCGEg\nREUbCtirBlCsJH95vOOh3rY3KsxtT/6vOm55j2OZaTAB1arLezBKNuXVgLTWzD4KjLEAqKXqf5pA\nrcEElLUSuH0UUCogBjSrbK8B1KOAokAIi0mu/1rGcbflsk/C1OCLrg89u16SlCfcvGe5j2RZqZQ8\nE5BRATCUVObh5TfB+tOO+q7HVwB4JqA4juuJ3dqsBA79eHmnKTQIAPf9gARA1naOeyo85RqC9TsT\nE5BJTECHK1t4/eHX8sS15/a2k0mt0Soy8YM/JBrAw84HphrA8LJx97LsdnwNpM4JjLcQqkEDaF1d\nKR3WAcgifQC5h5i1nfJK2HsdxUIhzQUUijBVjLixdhYmHnz9XGV8aXAC1xbaN1YmjvEVAJ4GUF8A\nI4mNfeXmuo3YpzkdNDS4AMSlPBigDyCvWlcxSlJBJAvBhOmCreqkgRxKD1TKMVV3E6sJSGlifE1A\nzukLXrriIDHtXPXt7N90qQEMzAQkAQuExLQ+mC6Hi1ss5la0dpuATlGg2QmsUUBKI5OhAWTF9Gfh\nx+Fm/CaIXBTQ4k7bv9i6qvEIrQDIQkRSJzDAdDFplxdSqihZNJiAVANQmhhjDaAeBtqgAbQjSwPw\nbEBB6kvofRD+zu89g0Jz9lAJqLbJz/KF6hnMy1beiKcBTPjCJqU3Nq4q8/SdG+AO1AmstDDGAqBW\nH7tTAdBh8GzwAbQunnEawGLCQGcycwcF2YXhLZ+qnQPAG1ENQFkcIsJpm1ZbAaBOYKWRCTEB9aEB\neALAhYkOMgqonQDwUQ1AWTTpvawagNLI+AoALwy0bs/vQQOQVg0gdBrAoE5bDwLg2FVljl87zY51\nM4PZtzI5bLdF+05c+kqsymgxviagRWkAGYnfPLtpGMet7frgmyvP54uPbuCN1Y92bFspxdxyzbkD\n2a8yYaw/dXxTfih9MSEawCJSODitwbObhn34ALJYc9r53H/Kvx7IthRFUXplsjSAXtLhZpiAotQE\nNBg7/CVnbOSSMzbC7QPZnKIoSk+MuQbgwkAXURM1aHWchfFgNQBFUZTlZHxHMi8b6KJMQNKaQCsq\nWAEwIB+AoijKctLXSCYiq0XkCyJyp/2/qk3bUES+KSJ/088+u2cRTmCfNiagzCyeS8AFp67n+LXT\nR2VfiqJMHv2OZNcCNxtjdgA32/d5vAHY3+f+uqdfJ7Cr0uPZ++PC0TUBfejSMzTyR1GUJaNfJ/BF\nwLn29ceAW4E3NzcSkY3AhcDvA1f3uc8uycoFlOO8fd034KG7Gj87711QXgWnPC/9KC4U7WbUBKQo\nyujTrwBYZ4y5x77+BbAup90fA/8GOHo1z/KygWYxty358ymvhPPe2fBRHBfbb0dRFGWE6CgAROQm\nYH3GV2/13xhjjIiYjN8/G7jPGPN1ETm3i/1dAVwBsHnz5k7N25DlA+gvfDPWKCBFUcaIjgLAGLMv\n7zsRuVdE5o0x94jIPHBfRrOzgeeKyAVACaiIyJ8ZYy7L2d8NwA0Au3fvbhEoXdOcDXQAg3asUUCK\noowR/Y5kNwKX29eXA59pbmCMeYsxZqMxZivwIuCWvMF/oDSEgYYDEQDFYlKQPVIBoCjKGNCvD+Dd\nwF+KyMuAnwIvBBCRDcB/McYsY/YpT3mQkEGs3i2Upvjn06/hxF0v6HtbDVz0IZg9drDbVBRF6UBf\nAsAYcz+wN+PznwMtg78x5laSSKGlpzkMdEB2+80XXTeQ7TRw+qWD36aiKEoHxtiW0eQEVsetoihK\nA+M7KvoaQBg35vpXFEVRJiQb6O6Xwsbdy3o0iqIow8b4CgA/DDRroZeiKMqEM8YmoFrfC78URVHG\nmfEVAL4JSFEURWlhfAWA7wRWFEVRWhhfAaAagKIoSlvGWACgGoCiKEobxlMAGJcGQgWAoihKHuMt\nAHT1r6IoSi7jOUK6Or5qAlIURcllPAUAagJSFEXpxHgKgNQEtLyHoSiKMsyMpwBQDUBRFKUj4ykA\nUg1ABYCiKEoe4ykAVANQFEXpyHgKAA0DVRRF6ch4jpAaBqooitKR8RQAagJSFEXpyHgKAHUCK4qi\ndGQ8BYBqAIqiKB0ZTwGgGoCiKEpHxlMAqAagKIrSkb4EgIisFpEviMid9v+qnHYrReSTIvJ9Edkv\nImf2s9+OaBiooihKR/odIa8FbjbG7AButu+z+I/A54wxJwFPAPb3ud/2qAlIURSlI/0KgIuAj9nX\nHwOe19xARGaBc4CPAhhjDhtjHuxzv+0JY9j5PFi9bUl3oyiKMspEff5+nTHmHvv6F8C6jDbHAb8E\n/puIPAH4OvAGY8xjWRsUkSuAKwA2b968uKMqVeCFH+vcTlEUZYLpqAGIyE0i8p2Mv4v8dsYYQ937\n6hMBu4D/bIw5HXiMfFMRxpgbjDG7jTG7165d21tvFEVRlK7pqAEYY/blfSci94rIvDHmHhGZB+7L\naHY3cLcx5jb7/pO0EQCKoijK0aFfH8CNwOX29eXAZ5obGGN+AdwlIifaj/YC3+tzv4qiKEqf9CsA\n3g2cJyJ3Avvse0Rkg4h81mv3OuDjInI78ETgD/rcr6IoitInfTmBjTH3k8zomz//OXCB9/5bwO5+\n9qUoiqIMFl0ppSiKMqGoAFAURZlQVAAoiqJMKGJMVuj+cCAivwR+utzHkcEa4FfLfRADRvs0Omi/\nRouj3a8txpiuFlENtQAYVkTkH4wxY+XU1j6NDtqv0WKY+6UmIEVRlAlFBYCiKMqEogJgcdyw3Aew\nBGifRgft12gxtP1SH4CiKMqEohqAoijKhDIRAkBENonI34rI90TkuyLyBvt5ZklLEZmz7R8VkQ80\nbasgIjeIyB22xOXFOfs8Q0S+LSI/FJH3iyTlyUTkansct4vIzSKyZZT7431/sYgYEVl0tMOw9UtE\nXugdyyfGoV8istlu+5v2Hrwg6/dD3K/fF5G7ROTRps+LIvIXtr+3icjWMelX3+NFW4wxY/8HzAO7\n7OsVwB3ATuAPgWvt59cC77Gvp4EnA68CPtC0rd8DrrevA2BNzj7/HthDUpn+fwPPsp8/DZiyr68E\n/mKU++Mdw98BXwN2j8l12gF8E1hl3x8zJv26AbjSvt4J/GTE+rXH7vfRps9fDfyJff0iFvFcDWm/\n+h4v2vZ1kBsblT+StNXnAT8A5r2L/oOmdr+TcUHvAqa7uIG+773/LeDDGe1OB7486v0B/hi4ELiV\nPgTAMPXLPuwvH7f7D/gw8Gb7+kzgK6PSr6b2zQPl54Ez7euIZOGVjHq/mr4byHjh/02ECcjHqoan\nA7fRXUlL/7cr7ct3icg3ROSvRCTrN8eSFMJx3G0/a+ZlJLOzRbPc/RGRXcAmY8z/WnQnso9tK8t7\nnU4AThCRL4vI10TkmYvrScuxbWV5+/UO4DIRuRv4LEmq9r45Sv1qx7Ekgy3GmAXgIWCux21kHdtW\nlrdfPn2PF81MlAAQkRngU8BVxpiH/e9MImI7hURFwEaSWdMu4KvAHy3yWC4jSZH97xfze7uNZe2P\niATA+4BrejnuLrY7DNcpIjEDnUsyg/6I90AviiHp128B/90Ys5EkZfuf2uu4aIakXwNnmPo1iPEi\ni4kRACISk1zMjxtjPm0/vleSUpZIfklLn/uBA4D7/V8Bu0QkFJFv2b93Aj8jufCOjfYzdyz7gLcC\nzzXGHBrh/qwAfgO4VUR+QmLHvFH6cwQPQ78gmTXfaIw5Yoz5MYkdeMcY9OtlwF8CGGO+CpRIctWM\nQr/a8TNgk91nBMza7S6KIerXQMaLPCZCAIiIAB8F9htj3ud91bGkpY+V+n9NMisEW97SGFM1xjzR\n/l1n1cSHRWSP3fdL3LZF5HQSO+xzjTGdbqCh7o8x5iFjzBpjzFZjzFYSJ/BzjTH/MMr9sr/5n+73\nIrKGxCT0T2PQr3+2v0NETiYRAL8chX51OBx/n5cAt9jt9sww9WsQ40VbBulQGNY/Eg+9AW4HvmX/\nLiCxEd4M3AncBKz2fvMT4NfAoySzwZ328y0kES+3299uztnnbuA7wI+AD1BfdHcTcK93HDeOcn+a\n2txKf1FAQ9MvkuiZ95HUr/428KIx6ddO4MvAP9rjOH/E+vWH9nc1+/8d9vMSyQz7hyQRUMePSb/6\nHi/a/elKYEVRlAllIkxAiqIoSisqABRFUSYUFQCKoigTigoARVGUCUUFgKIoyoSiAkBRFGVCUQGg\nKIoyoagAUBRFmVD+P3YmJ3rWZMBBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5c9707b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(arma.fittedvalues)\n",
    "plt.plot(train[1:])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 作业\n",
    "根据ARIMA模型对其他股票收益率做预测。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
